10.4 Sediment Transport

10.4 Sediment Transport T Aagaard and M Hughes University of Copenhagen, Copenhagen K., Denmark, and University of Sydney, Sydney, NSW, Australia r 2013 Elsevier Inc. All rights reserved.

10.4.1 10.4.2 10.4.2.1 10.4.2.2 10.4.2.3 10.4.3 10.4.4 10.4.4.1 10.4.4.2 10.4.4.3 10.4.4.4 10.4.4.5 10.4.4.6 10.4.5 10.4.6 10.4.7 References

Introduction Measuring Nearshore Sediment Transport Measurement Devices for Suspended Load Measurement Devices for Bedload Measurement of Total Sediment Transport Sediment Mobilization and Suspension Cross-Shore Sediment Transport Transport Mechanisms The Cross-Shore Distribution of Suspended Sediment Transport Cross-Shore Suspended Sediment Transport on Dissipative, Intermediate, and Reflective Beaches Sediment Transport in 3D Morphological Settings The Role of Bedload Transport Numerical Models of Cross-Shore Sediment Transport and Beach Profile Change Longshore Sediment Transport Swash Zone Sediment Transport Concluding Remarks

Glossary Acceleration skewness The third-order moment of instantaneous fluid acceleration, du3t /dt. It is associated with an asymmetry of the wave shape about the vertical axis and typically occurs under sawtooth-shaped bores in the surf zone. Boundary layer streaming A (Eulerian) net current in the wave boundary layer, generated by the oscillatory flow. Expansion and contraction of the bottom boundary layer associated with the passage of waves create weak vertical flows. Due to the presence of the seabed, the horizontal and vertical flows in the boundary layer are not 901 out of phase, and the time-averaged product of horizontal (u) and vertical (w) flows is nonzero over a wave period. This generates a shear stress (t¼ uw) on the fluid particles, which results in a weak, generally onshore-directed, mean current. Gravity waves They are generated by the wind and comprise wind waves and swell. They have wave periods between 1 and 20 s (0.05–1 Hz) and their main restoring force is gravity. Infragravity waves They have periods between 20 and 200 s (0.005–0.05 Hz) and they are forced directly or indirectly by groups of gravity waves. Bound long waves are locally forced (infragravity) waves that are bound to and propagate with groups of gravity waves, whereas two-dimensional standing (infragravity) waves and three-dimensional (infragravity) edge waves are free waves that are reflected against the shoreline and form cross-shore, standing wave patterns.

75 76 76 78 78 79 82 82 87 88 88 90 90 91 93 101 101

Lagrangian/Eulerian reference frame There are two fundamental ways to describe fluid flow. One is the Lagrangian description that tracks each fluid particle at all times. For example, the Stokes drift can only be resolved in a Lagrangian reference frame. The other is the Eulerian description, where the fluid motion is specified at a fixed point in the water column. Spatially fixed instruments (current meters) can only resolve the Eulerian velocity. Stokes drift A (weak) onshore-directed mean current that arises because the fluid particle orbits are not closed under waves. The wave orbital diameter depends inversely on distance below the mean water surface and it is therefore larger under wave crests than under wave troughs. This leads to a slow onshore drift of the fluid particles. The name is associated with the British mathematician G. G. Stokes who introduced a theory for finite-amplitude waves. Another term for this phenomenon is Lagrangian drift. Velocity skewness The third-order moment of instantaneous fluid velocities, u3t . It is associated with an asymmetry of the wave shape about the horizontal axis. As waves shoal, wave crests become narrow and peaked, whereas wave troughs become wide and shallow. Fluid velocities become larger under wave crests than under wave troughs and seen over a wave period, and the velocity skewness becomes positive (i.e., onshore directed).  3  /u S Normalized velocity skewness is expressed as /u2 St 3=2 , t where /S indicates the time-average.

Aagaard, T., Hughes, M., 2013. Sediment transport. In: Shroder, J. (Editor in Chief), Sherman, D.J. (Ed.), Treatise on Geomorphology. Academic Press, San Diego, CA, vol. 10, Coastal Geomorphology, pp. 74–105.

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http://dx.doi.org/10.1016/B978-0-12-374739-6.00273-6

Sediment Transport

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Abstract Sediment transport is the mechanism that translates the work of hydrodynamic processes into morphological change. This chapter discusses the transport of noncohesive sediment in wave-dominated settings. Following an introductory section, techniques for measuring sediment transport are described, providing context for the following sections. Section 10.4.3 discusses the physical mechanisms that mobilize and suspend sand into the water column. Processes resulting in cross-shore (onshore/offshore) sediment transport, and ultimately beach erosion and accretion, are described in Section 10.4.4 and longshore sediment transport in Section 10.4.5. Finally, sediment transport in the swash zone is discussed in Section 10.4.6.

Introduction

Sediment transport is the process that provides the coupling between hydrodynamic processes and beach morphology. Without any transport of sediment, there would be no morphological change and there would be no beaches. The relationship between sediment transport and morphological change is described by the sediment conservation equation:   dz dq dC ¼  þ dt dx dt

½1

where z is the bed elevation, q is the sediment transport rate, C is the amount of sediment in the water column (the sediment load), t is the time, and x is the distance in the direction of transport. The first term on the right hand side of eqn [1] states that a positive gradient in sediment transport rate along the transport path results in a lowering of the seabed along that path over time, whereas a negative transport gradient leads to accretion. The second term on the right hand side of the equation describes the temporal change in the amount of sediment kept in suspension above the seabed. This term can be ignored if the timescale considered is longer than a few wave cycles (seconds or minutes), because sand is rarely kept suspended in the water column for longer periods of time. This chapter provides a discussion of noncohesive sediment transport in the nearshore with a focus on the transport of sand- and gravel-sized sediment under the influence of wave action. The nearshore is defined here as consisting of the lower shoreface, the upper shoreface, and the beach face (Figure 1). Different wave regimes dominate across the nearshore, resulting in distinctly different sediment transport characteristics. The lower shoreface is dominated by shoaling wave processes, and wind- and tide-generated currents are additional significant contributors to the transport of sediment. The morphologically active upper shoreface, generally containing one or more nearshore bars, is dominated by breaking wave processes in the surf zone. In addition to waves incident from offshore, secondary, low-frequency waves, and mean currents generated by the processes of wave breaking are responsible for the movement of sediment. Finally, the beach face is affected by the high-velocity uprush and backwash flows of the swash zone, which produce large landward- and seaward-directed transport rates. Coarse sediment such as gravel is typically transported as bedload, when grains roll, slide, or hop along the bed, whereas the finer sand fraction can also be suspended in the water column and carried along with the flow. The strongly oscillatory velocity field under waves means that individual sand grains can be subjected to any of these transport states at

various instants in time. Grains may also come to rest at or in the bed, only to be exposed and/or transported during the next wave cycle. Any exclusive mode of sand transport is difficult to identify in the nearshore (Hanes, 1988), so for convenience the transport mode is generally classified as either (1) dominantly bedload where the sediment grains are moving in contact with the bed and are supported by other grains, or (2) dominantly suspended load where the grains are supported by turbulence in the surrounding fluid (Bagnold, 1966). An approximate threshold that distinguishes bedload from suspended load is a volume concentration of 0.08 m3 m3 (corresponding to about 140 g l1), above which significant intergranular collisions occur and bedload dominates (Komar, 1998). Another generally applied simplification is the separation of the sediment transport vector into cross-shore and longshore components relative to the orientation of the shoreline or to the depth contours. This makes transport concepts and modeling much more tractable, and the sediment conservation equation is then generally modified to: dz dqx dqy ¼   dt dx dy

½2

where qx is the cross-shore sediment transport rate, and qy is the longshore sediment transport rate, and x and y are the cross-shore and longshore coordinates. In most cases both terms on the right hand side of the equation are nonzero and sediment is transported obliquely to the orientation of the shoreline. Note that the temporal variation in sediment load (eqn [1]) has been ignored here.

Upper shoreface surf zone

Lower shoreface shoaling wave zone

4 Elevation (m)

10.4.1

MWL

0 −4 −8

Beach face swash zone

−12 0

1000 2000 Distance from shoreline (m)

3000

Figure 1 Schematic diagram of the nearshore showing the morphological and hydrodynamic zones considered in this chapter. MWL is mean water level. Note that elevations and distances are not absolute.

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10.4.2

Measuring Nearshore Sediment Transport

Measurement of sediment transport under waves is not a trivial task because of the different modes of transport, reversing flows, generally high-energy conditions which make instrument deployment and maintenance difficult, and large sediment transport gradients that make for a highly dynamic seabed that rarely remains in the same vertical position for long periods of time. Furthermore, despite the fact that great strides have been made recently, instruments and equipment for measuring sediment transport still suffer from various limitations and several complementary techniques must commonly be employed.

10.4.2.1

Measurement Devices for Suspended Load

One of the first to investigate suspended sediment concentration under waves was Watts (1953) who used suction pumps, originally devised for measuring sediment transport in rivers, to determine mean suspended sediment concentration profiles. Suction pumps and bottle sampling have since been used by Nielsen (1984) and Kroon (1991), for example. A comprehensive study on the efficiency of pump samplers was performed by Bosman et al. (1987), who found that pump sampling yielded satisfactory results, provided that pump intake velocity exceeds the ambient flow by a factor of three. Given the relatively small and strongly time-varying sediment concentrations in the water column throughout most of the nearshore zone, the sampling bottles need to be large to yield a reliable measure of mean sediment concentration over a reasonable timescale. An alternative method for sediment trapping and for directly computing sediment transport rates was introduced by Hom-ma and Horikawa (1962) and later refined by Kraus (1987). The measurement devices are called streamer traps, and they consist of a vertical array of polyester, sieve cloth bags that are mounted on a stainless steel rack. The traps are carried manually to the deployment site where samples are taken over a time frame of 5–10 min. The contents of the bags are then dried and weighed. Field deployments indicate that the traps provide consistent and robust estimates of longshore and crossshore transport rates (Kraus and Dean, 1987; Brander, 1999). However, the technique is limited to favorable (relatively shallow) water depths and wave heights (relatively small) inside the surf zone. It can only be used under low-energy conditions and in situations where unidirectional currents are sufficiently strong to avoid entangling the bags, thus limiting the technique to measurements of longshore transport and cross-shore transport in rip currents under relatively small waves. The technique has also proved useful in the swash zone to separately quantify uprush and backwash sediment transport during single swash events (Hughes et al., 1997a). Although trap-based techniques are useful for estimating the amount of sediment carried by mean currents, they cannot resolve the time-dependent nature of sediment concentration nor the transport due to oscillatory wave motions. Measurement devices for both flow velocity and suspended sediment concentration have become increasingly sophisticated, and are now capable of measuring suspended sediment transport due

to both mean and oscillatory flows using the following relationship. The instantaneous suspended transport rate, qs(t) at a given elevation above the bed, z, is the product of sediment concentration, c, and the velocity by which the grains are transported by the fluid, ug, qs ðtÞ ¼ ug ðtÞcðtÞ

½3

The equation can be integrated over the timescale of interest and over water depth to yield the net suspended sediment transport rate. It is generally assumed that ug ¼ u, where u is the speed of the surrounding fluid. Although approximately true for fine sand (or smaller grain sizes), the assumption becomes increasingly difficult to justify for medium and coarse sand. Techniques to resolve the time-dependent nature of suspended sediment concentrations (eqn [3]) began when Brenninkmeyer (1976) deployed an optical transmissometer to measure the attenuation of light due to suspended particles. Downing et al. (1981) later introduced an improved device; the optical backscatter sensor (OBS) that is smaller in size and less sensitive to air bubbles in the water. The OBS-sensor works by emitting an infrared light that is reflected and backscattered by sediment in the water. The backscattered signal is detected by a photodiode and transformed to a voltage, which is a linear function of sediment concentration. The rapid frequency response (sampling rates of 10–20 Hz can be achieved, depending on exact sensor type) of the OBS means that they are capable of resolving the detailed features of fluctuating sediment concentration under waves. The instruments can be deployed in vertical arrays to resolve sediment concentrations through the water column over long periods of time. Consequently, they have been widely used for suspended sediment concentration and transport measurements in the nearshore. An example of a sediment concentration time series obtained from an OBS deployed close to the bed in the inner surf zone is illustrated in Figure 2. Sediment concentration and velocity were recorded at 10 Hz and sediment response to sequences of large and small waves is evident. It is abundantly clear, however, that there is no straightforward relationship between sediment concentration and velocity magnitude. Despite the general success of OBS-sensors in providing realistic, quantitative measures of suspended sediment concentration, they do suffer from several shortcomings. The output voltage depends not only on sediment concentration, but also on sediment grain size and color (Black and Rosenberg, 1994; Battisto et al., 1999; Hatcher et al., 2000; Downing, 2006). Therefore the sensors must be calibrated with the local sediment at the deployment site, ideally with a sample of the sediment in active suspension. The sensor sampling volume decreases with increasing sediment concentration, and because sensor diameter is typically about 15 mm, care must be taken when deploying these instruments near the bed. At elevations less than 40–50 mm, the sensors can create turbulence and artificially enhance sediment suspension. Sensors are typically deployed in a spatially fixed position, so if the seabed accretes or erodes, the vertical sensor positions need to be adjusted or measured frequently in order to provide reasonable estimates of sediment concentration profiles and

Sediment Transport

2

80 1 60 0 40 −1

20

−2

0 1900

Velocity (m s−1)

Sediment concentration (g l−1)

100

77

1950

2000

2050

Time (s) Figure 2 Time series of cross-shore velocity (thick line) and suspended sediment concentration measured at 10 cm above the bed (thin line). Data were recorded in the surf zone at Vejers on the Danish North Sea coast. The water depth at the instrument station was 1.32 m and the significant wave height was 0.82 m.

transport (Ogston and Sternberg, 1995). Finally, the OBS is sensitive to air bubbles and foam, which may increase sensor outputs by 25% (Puleo et al., 2006). Care must therefore be taken when interpreting OBS-signals obtained under breaking waves in the inner surf zone, or in the highly aerated swash zone. To overcome some of these instrument deficiencies, smaller fiber-optic backscatter sensors (FOBS) were developed (Beach et al., 1992). The diameter of these sensors can be made as small as a few mm, and therefore vertical sensor arrays can be deployed very close to, and, indeed, into the seabed (Foster et al., 2000; Aagaard et al., 2005; Austin and Masselink, 2008). By using laser diodes, some sensor types, such as the UFOBS-7 (Downing, 2006), sample sediment concentrations in fixed sampling volumes located some distance away from the sensor head. Problems with sensitivity to air bubbles have not been identified with this latter type of sensor (Aagaard and Hughes, 2006), but clearly the deployment of such instruments still represents a physical intrusion in the bottom boundary layer. Instantaneous sediment concentration measurements obtained with vertical arrays of OBS-sensors (such as illustrated in Figure 2 for a single sensor) can be paired with measurements of ambient fluid velocity from colocated fast-response current meters (Figure 3) to provide estimates of the net suspended sediment flux (eqn [3]). The resulting transport estimates can then be split into transport contributions from mean flows and waves using the uc-integral concept (Jaffe et al., 1984): hqs i ¼ huci ¼ huihci þ u0 c0

½4

where u is the instantaneous fluid velocity and c is the instantaneous sediment concentration. Brackets denote timeaveraged quantities and primes represent oscillatory terms. Huntley and Hanes (1987) demonstrated how the u0 c0 term in eqn [4] can be resolved in frequency space, by using cospectral techniques, to obtain information on sediment transport rates and directions associated with different wave frequencies.

Figure 3 Arrays of OBS and FOBS sensors deployed on a stainless steel H-frame with an electromagnetic and an acoustic current meter. A second instrument station is submerged in the background, and the photo was taken at low tide.

The introduction of acoustic backscatter sensors (ABS) overcame some of the disadvantages associated with OBSsensors by providing the capability of obtaining remote measurements of suspended sediment concentration continuously through the water column at a resolution as fine as about 5 mm, with sampling rates of several Hz (Hay and Sheng, 1992; Osborne et al., 1994). When two or more sensors with different acoustic frequencies are deployed, estimates of suspended sediment grain size can be made (Crawford and Hay, 1993). The drawback with ABS-sensors is their very high sensitivity to air bubbles (Hanes et al., 1988) and the intricate algorithms required to invert the backscattered signal to obtain sediment concentration (Sheng and Hay, 1988; Thorne and Hanes, 2002; Betteridge et al., 2008). Nevertheless, these sensors are seeing increased use, particularly in deep water and/or on the lower shoreface where bubbles from wave breaking do not penetrate to the sensor sampling depths

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Elevation above the bed (m)

0.4

0.3

0.2

0.1

0 0.01

0.1 1 Sediment concentration (g l−1)

10

Figure 4 Profile of suspended sediment concentration calculated from a pulse-coherent acoustic Doppler profiler. Measurements were obtained under nonbreaking waves in a bar trough. Wave ripples on the seabed had a wavelength of l¼11 cm and a height Z¼2 cm.

(Traykovski et al., 1999; Cacchione et al., 2008; Dolphin and Vincent, 2009). Acoustic/Coherent Doppler Profilers (ADP/ CDP; Zedel and Hay, 1999; Newgard and Hay, 2007; Ha et al., 2011) offer some of the same possibilities as the ABS with the added advantage that colocated velocity measurements for sediment transport calculations are obtained. Figure 4 shows a mean sediment concentration profile obtained with a pulse-coherent ADP under shoaling waves and on a rippled bed. It should be clear from the preceding discussion that perfect sensors for quantitative measurements of suspended sediment concentration and transport in the field do not yet exist. However, reasonable estimates can be made and the techniques are more robust and reliable than techniques for estimating bedload transport.

10.4.2.2

Measurement Devices for Bedload

Early studies of bedload transport used sediment tracer techniques (e.g., Ingle, 1966; Komar and Inman, 1970), which involved the injection of tagged sediment grains and a tracking of their dispersal in the direction of transport. The technique has mainly been applied to study longshore transport, and the bedload transport rate (qb) is given by X qb ¼ vðxÞbðxÞDx ½5 x

where v(x) is the advection velocity of the tracer at a given cross-shore coordinate, x, and b is the mixing depth of the tracer (Madsen, 1989; White and Inman, 1989). Estimates of net longshore (bedload) sediment transport are obtained by integrating qb across the surf zone. Considerable effort has been invested in attempting to develop predictive equations for tracer mixing depth (e.g., Kraus, 1985; Ciavola et al., 1997), however, several problems exist with the tracer technique. For example, it is not clear how tracer diffusion caused

by oscillatory flows should be interpreted in terms of a net transport, and it is not clear that the assumption that advection velocity is uniform over the entire mixing depth is valid. Moreover, it was originally assumed that tracer dispersal is exclusively a measure of bedload transport (Komar and Inman, 1970). This, probably erroneous, assumption was made on the basis that suspended sediment transport is characterized by more or less permanent suspension of the particles. This is certainly not the case under waves (Hanes, 1988; see also Figure 2), so tracer techniques should at best yield an estimate of bedload plus some/most suspended load transport. A methodology that has shown some promise for the estimation of bedload transport is the remote imagery of the seabed geometry and measurement of bedform migration rates using sonars (Greenwood et al., 1993). The determination of bedload transport rates from this technique relies on the assumption that bedform migration rate is directly comparable to bedload transport (Hay and Bowen, 1993; Traykovski et al., 1999). Hoekstra et al. (2004) obtained agreement within a factor of two between estimated bedload transport determined by bedform migration as recorded by a ripple profiler and model predictions from a numerical bedload transport model. However, the method is only applicable in situations when distinct bedforms appear on the seabed. Moreover, it is not clear to what extent suspended load might contribute to bedform migration. For laboratory measurements, Ribberink and Al-Salem (1995) developed a conductivity concentration meter that measures sediment concentration in the bedload layer. The measurement principle uses the difference in conductivity between water and sediment and through calibration, the relative quantity of the two phases can be determined. A system consisting of two such probes was used by McLean et al. (2001) to estimate bedload transport, based on the crosscorrelation signal between the two probes. The sensors, which have a diameter of about 4 mm, are inserted through the bottom of a flow tunnel or a wave flume and point upward through the bed. These devices rely on very precise positioning to resolve the bedload layer at mm-scale and would require almost continuous re-positioning on a dynamic natural beach, making them impractical for field measurements. The development of devices for bedload measurement is still in its infancy and remains a priority research issue.

10.4.2.3

Measurement of Total Sediment Transport

Determination of temporal bed-level changes and the direct application of the sediment conservation equation (eqn [1]) can be used to estimate indirectly the total transport of sediment, i.e., the sum of bedload and suspended load. Bed-level changes can be determined using conventional survey techniques (Dean et al., 1987), rods inserted into the seabed (Greenwood and Hale, 1980), electromagnetic bed-level sensors (Ridd, 1992; Aagaard et al., 2001), or acoustic devices installed at some distance above the seabed (Thornton et al., 1998). In the intertidal and swash zones, buried pressure sensors (Baldock et al., 2005) and ultrasonic altimeters (Blenkinsopp et al., 2011) have been used to resolve bed-level

Sediment Transport

10.4.3

Sediment Mobilization and Suspension

Sediment is mobilized by friction between the moving fluid and the sediment grains resting on the seabed. In the bottom boundary layer, friction generates small turbulent vortices that set up stresses between fluid and grains, termed bed shear stresses. The bed shear stress is a quantity that is of major importance in determining the way sediment reacts to fluid forcing. A rigorous definition of the bed shear stress is t ¼ r(u00 w00 ) where r is the fluid density, and (u00 w00 ) is the Reynolds stress which is the product of turbulent horizontal (u00 ) and vertical (w00 ) velocities in the bottom boundary layer. Until recently, this formulation has seen little use in wave-dominated environments, because it has been difficult to measure a threedimensional (3D) velocity field in thin wave boundary layers at the high frequencies required to resolve the turbulent velocity components. An alternative and more conventional definition of the bed shear stress reads t ¼ ru2 , where u is the friction velocity at the bed and it depends on the near-bed velocity gradient du/dz. In the nearshore, peak wave orbital velocities are, in most circumstances, faster than mean current speeds, and because of the reversing nature of the flow, wave boundary layers are much thinner than current boundary layers. Consequently, velocity gradients in the wave boundary layer are generally much steeper than in current boundary layers. Waves therefore generate more bed friction and larger bed stresses, and thus they are the main mechanism responsible for stirring sediment in the nearshore. The thickness of the wave boundary layer is generally on the order of 0.10 m or less. Shear plates have recently been used in the laboratory to directly measure the bed shear stress (Barnes et al., 2009), but such equipment is too fragile to use in field settings. A common circumvention of the problem has been to define the bed shear stress under waves as t ¼ ½rfw u2

½6

where u is the maximum horizontal free-stream velocity in the wave cycle (at the top of the wave boundary layer) and fw is a wave ‘friction factor,’ or a transfer function between free-stream velocity and friction velocity. The friction factor is often specified after Jonsson (1966) or Swart (1974). The latter expression reads: !  0:194 ks  5:977 ½7 fw ¼ exp 5:213 A where fw is expressed as a function of orbital amplitude (A¼uT/2p, where T is the wave period) and bed (grain)

roughness (ks ¼ 2.5D, where D is the mean sediment grain size) with additional terms added when ripples exist on the seabed (see Nielsen, 1986, 1992). For nearshore oscillatory flows over sandy beds, calculated wave friction factors are typically of the order of 0.01. The abovementioned parameterizations of fw were developed from laboratory experiments over fixed beds and it could be questioned how well such conditions represent the real world. Moving sand grains increase the roughness above that expected for fixed grains. In addition, since the dynamic forcing that generates bed friction is expressed exclusively through orbital amplitude, the parameterizations do not take into account turbulence generated by other sources, for example wave breaking, which in some cases can penetrate to the seabed (Cox and Kobayashi, 2000; Aagaard and Hughes, 2010). Smyth et al. (2002) used a coherent acoustic Doppler profiler and the Reynolds stress concepts to introduce a method to derive the friction factor directly from near-bed measurements of (turbulent) vertical and horizontal flows:  00 2 2w ½8 fw ¼ 2 u where w00 is the vertical turbulent flow component and u is the horizontal velocity vector. Friction factors are typically larger for breaking than for nonbreaking wave conditions because of the vertical flux of horizontal momentum into the boundary layer caused by turbulence associated with wave breaking (Feddersen et al., 2003). Inner surf-zone field measurements of the ratio of fw determined from eqn [8] to fw determined from the Swart-equation (eqn [7]) are shown in Figure 5. The ratio between the two expressions for fw ranged from 2 to 10 and it increased with local relative wave height, the latter being 10

8

fw/fw; Swart

changes and sediment transport gradients at high temporal and spatial resolution. In order to resolve both the magnitude and direction of the transport bed-level measurements at several positions are required. In the case of a cross-shore transect (assuming no longshore transport) there must also be closure (no bed elevation changes) at one end of the profile. In the case of a 2D array of measurements there must be closure along two boundaries of the array.

79

6

4

2

0 0

0.4

0.8

1.2

Hs h−1 Figure 5 The ratio between friction factors fw determined from eqn (8), and the Swart friction factor (eqn [7]) as a function of relative wave height Hs/h. Measurements were obtained in an inner surf zone with breaking waves. Adapted from Dohmen–Janssen, C.M., Hanes, D.M., 2002. Sheet flow dynamics under monochromatic nonbreaking waves. Journal of Geophysical Research 107(C10), 3149, doi:10.1029/2001/JC001045, with permission from American Geophysical Union.

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a measure of the ability of wave-generated surface turbulence to reach the bed. Turbulence injected from wave breaking therefore appears to be a significant added source of bed shear stress in shallow water depths on the upper shoreface. The mobilization of bed sediment by waves can be estimated using the Shields parameter, which is a nondimensional expression for the bed shear stress and is defined as y¼

t rðs  1ÞgD

½9

where s is the relative sediment density. Based on field and laboratory experiments, Nielsen (1986) found that the threshold of sand motion occurs for ywE0.05, where the subscript denotes the Shields parameter calculated for wave motion only. This is a value that is typically assumed in applications, but the uncertainties involved in calculating the bed shear stress in eqn [9] make the procedure of using a threshold Shields parameter less than straightforward. Green (1999) used orbital velocity measurements and a video camera to test the threshold velocity equation proposed by Komar and Miller (1973):  ½ u2 A ¼ 0:21 D ðs  1ÞgD

½10

Using ‘significant’ orbital velocity to arrive at orbital amplitude, Green (1999) found that this equation is a good predictor of initial sediment movement outside the surf zone and it circumvents the difficulties of using the Shields parameter approach. The methodology expressed by eqns [10] and also [9], when fw is specified by the Jonsson/Swart approach (e.g., eqn [7]), assumes that sediment stirring is a function of orbital velocity magnitude and grain size only. An increasing body of literature indicates that wave shape, causing fluid accelerations and decelerations, also has an impact on sediment mobilization (e.g., Chapter 10.3, this volume). For example, Foster et al. (2006) provided field evidence suggesting that pressure gradients derived from fluid accelerations under asymmetric waves were important to the incipient motion of sediment. The observed thresholds of sediment mobilization under asymmetric waves were smaller than predicted using equations that consider exclusively horizontal fluid velocity. Moreover, shear stresses generated by mean currents, although being subordinate in most cases, are clearly not negligible and they interact nonlinearly with wave-generated, bed shear stresses, thus enhancing the total bed shear stress. Models for bed shear stresses in combined wave–current boundary layers have been proposed by Grant and Madsen (1979) and Soulsby (1997). Once the sediment grains have been mobilized, they can move as grain-supported bedload, either in a sheet flow layer where the volumetric concentration decreases from CE0.6–0.7 in the stationary bed to CE0.08 (where intergranular forces become unimportant), or in a layer corresponding to the height of migrating bedforms (Hoekstra et al., 2004). In the sheet flow case, the bedload layer is on the order of 10 grain diameters thick and the thickness increases with bed shear stress (Dohmen-Janssen and Hanes, 2005). Above the moving bed layer, sediment moves in intermittent

suspension where the grains are principally supported by the surrounding fluid. Lifting of sediment grains into suspension occurs when turbulent fluctuations near the bed become sufficiently large, and it is generally assumed that this occurs when the ratio between friction velocity and grain settling velocity increases above unity. The upward mixing of sediment in the water column can occur either through diffusion of the suspension or as convection, in which case the sand grains are lifted as more or less coherent clouds of sediment. Convection dominates when steep ‘vortex’ ripples (Bagnold, 1946) are present on the bed and vortex shedding occurs from these bedforms. The generation of small sediment-laden vortices typically takes place in the lee of steep bedforms at orbital velocity maxima under wave crests and wave troughs, and these vortices are subsequently ejected from the bed at velocity reversals (Nakato et al., 1977; Osborne and Greenwood, 1993; van der Werf et al., 2008; Mignot et al., 2009). The vertical distribution of suspended sediment, averaged over several wave periods, can be described by the timeaveraged sediment convection-diffusion equation:

ws CðzÞ þ es

dc ¼0 dz

½11

where C is the (mean) sediment concentration, z is the vertical distance above the bed, and the overbar indicates waveaveraged terms. The equation states that the upward mixing of sediment, expressed through a ‘sediment diffusivity,’ es, is balanced by sediment settling, expressed by the sediment fall velocity, ws. Several expressions for es exist in the literature and one of the most recent formulations was proposed by Van Rijn (2007). It is likely that sediment diffusivity scales with nearbed turbulent velocity and the rate at which this turbulence is produced; such that large waves, short wave periods and fine sediment grain sizes result in large diffusivities and mean concentration profiles where sediment concentration decreases relatively slowly with distance above the bed. A more rapid decrease in sediment concentration above the bed will then occur for smaller, long-period waves and coarse grain sizes, where the sediment diffusivity will be small. The micromorphology of the seabed also affects sediment diffusivity and larger values of es are observed with wave ripples than with flat beds (Vincent and Downing, 1994). This is partly because of the larger roughness elements that cause additional turbulent vortex generation over ripples. Wave breaking is another mechanism that affects sediment diffusivity. In shallow water depths and particularly when waves are plunging, surface-generated turbulence can reach the bed and may significantly increase sediment concentration/diffusivity and sediment transport (Kana, 1978; Yu et al., 1993). In a recent study, Aagaard and Hughes (2010) observed that wave impact on the bed can generate large sediment clouds, and under plunging waves in the breaker zone up to 85% of the suspended sediment load in the water column may be associated with large vortices generated by wave breaking. When a breaking wave vortex hits the bed, clouds of sediment are lifted upward in a convective process, and such clouds may be advected several meters away from the

Sediment Transport

breakpoint before sediment settles out (Black et al., 1995; Beach and Sternberg, 1996). The shape of the suspended sediment concentration profile depends on the process that dominates the upward mixing of the sediment grains. When convection is dominant, for example, due to vortex shedding from bedforms or breaker vortices lifting the sediment in coherent packages, vortex size and intensity is near-constant over the lower part of the water column and sediment diffusivity is therefore near-constant in the vertical. Mean sediment concentration profiles will then take on an exponential shape. In cases when diffusion dominates, turbulent vortices generated by bed friction expand as they propagate upwards; diffusivity then increases linearly with height and mean suspended sediment concentration profiles approximate a power-function (Dolphin and Vincent, 2009). It is clear that the theoretical descriptions of sediment mobilization and the vertical distribution of sediment concentration (e.g., eqn [11]) are oversimplified. Figure 2 illustrated the seemingly erratic nature of sediment suspension under strongly breaking waves in the surf zone. Figure 6 shows a contrasting example of sediment concentrations recorded under shoaling waves at 8 m water depth on the lower shoreface, and under these less complex conditions there is still no straightforward relationship between orbital velocity and sediment concentration. The time series shown in Figures 2 and 6 also demonstrate the strongly time-dependent nature of sediment suspension under natural conditions. It is clear that no single process can explain the variability in concentration magnitude, but that many processes interact. The following is a list of factors that have been demonstrated to affect near-bed sediment concentrations during field experiments:

4.

5.

6.

in vertical grain size fractionation. Under full-scale shoaling waves in a laboratory wave flume, Greenwood and Xu (2001) observed an 18% decrease in mean grain size between elevations of 4 and 24 cm above the bed. Bedforms – ripples on the seabed enhance bed shear stresses and both vertical mixing lengths and sediment diffusivities are much larger when the bed is rippled than when it is flat. With flat beds, sediment diffusivity is relatively smaller and the suspended sediment may be confined to the lower tens of mm of the water column where the sediment moves in a high-concentration, carpet-like sheet flow. Bedforms further affect the phase relationship between fluid velocity and sediment concentration in a nontrivial way, especially under irregular waves. Wave groups – a successive ’pumping up’ of sediment occurs under groups of large waves, because of the finite sediment settling velocity, leading to much larger sediment concentrations at the end of a wave group than at the beginning of a group (Hanes, 1991; Osborne and Greenwood, 1993; Williams et al., 2002). Wave breaking – the added turbulence due to wave breaking creates additional bed shear stress and vertical sediment mixing (Yu et al., 1993; Scott et al., 2009). Under plunging breakers, large vortices with vertical velocities up to 1 m s1 have been observed in the field, and they can lift large clouds of sediment upward from the bed (Aagaard and Hughes, 2010). However, vortices from spilling breakers are much more limited in vertical extent and rarely reach the bed. Consequently, sediment loads under plunging waves are typically larger than under spilling waves (Kana, 1978). Infragravity waves can become very energetic in the inner surf zone where they may contribute significantly to sediment suspension, as suggested by modulations of the sediment concentration magnitude at time scales of 20–100 s (Russell, 1993; Aagaard and Greenwood, 1995a).

Attempting to disentangle and model the contributions from each of these processes – and probably more – is a major task and bulk parameterizations may presently prove more successful. Another complication is phasing of sediment concentration relative to fluid velocity (Figures 2 and 6). Instantaneous

10

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Velocity (cm s−1)

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1. Fluid velocity – larger (horizontal) fluid velocities, whether of wave or current origin, enhance the bed shear stress and therefore mobilize and suspend larger amounts of sediment. The coexistence of waves and currents results in nonlinear enhancement of the total shear stress and sediment mobilization. 2. Sediment grain size – finer sediment is more easily suspended and mixed upward in the water column. Furthermore, a distribution of grain sizes exists in the bed and the finer grains will be suspended to larger elevations, resulting

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Time (s) Figure 6 Time series of cross-shore velocity (thick line) and suspended sediment concentration at 5 cm above the bed (thin line), recorded at 7.6 m water depth off the Danish North Sea coast. The significant wave height was 1.32 m and the sampling frequency was 2 Hz.

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suspended sediment concentrations (and sediment concentration profiles) under waves fluctuate continuously over a wave period, and the way that instantaneous concentration (c(t)) is related to instantaneous fluid velocity (u(t)) is of critical importance to the direction and net magnitude of sediment transport. Increasing time lags often exist between fluid forcing and sediment concentration for increasing elevations above the bed, because of the time it takes for sediment to respond to fluid motion and mix upward in the water column. Such time lags significantly impede our ability to predict (suspended) sediment transport rates. Not only do the time lags depend on elevation above the bed, but they also depend on the shape of the bed. There are relatively small time lags for flat beds and large phase lags when ripples and vortex shedding occurs (Osborne and Greenwood, 1993). Very detailed laboratory measurements of phase relationships between fluid velocity and sediment concentrations in and above the bed were obtained under regular, monochromatic, nonbreaking waves in a large wave flume by Dohmen-Janssen and Hanes (2002). The waves were strongly skewed with large velocities under the wave crest (Figure 7). Their measurements indicate that sediment was almost exclusively mobilized under the wave crest, and in the bedload layer, sediment concentrations were nearly in phase with fluid velocity. A significant time lag relative to the fluid forcing was introduced for the suspended sediment, and for elevations above 18 mm, maximum concentrations appeared on the offshore wave stroke leading to offshore transport of sediment. Dohmen-Janssen and Hanes (2002) also observed that time lags increase for fine sand and short wave periods. It is likely that such time lags become less systematic with natural waves, further complicating a detailed description and modeling of sediment mobilization and transport.

10.4.4

Cross-Shore Sediment Transport

The fluid velocity required to transport sediment in the nearshore (eqn [4]) can be produced by a variety of hydrodynamic processes, some of which are dominant in the cross-shore dimension and some of which are dominant in the longshore dimension. This section discusses crossshore transport. In most cases, spatial gradients in crossshore sediment transport are much larger than longshore transport gradients and therefore the configuration and morphologic change of the nearshore profile over time is a reflection of the integrated result of cross-shore sediment transport processes. Because of instrumental constraints, experimental work has dealt mainly with suspended sediment transport rather than bedload transport and consequently most of the following will address suspended load. A more specific discussion of the aspects of bedload transport will follow separately in Section 10.4.4.5. Despite the difficulties just described with modeling the detailed mechanics of sediment transport under waves, crossshore sediment transport and the process mechanisms involved in that transport are fairly well understood in a qualitative sense.

10.4.4.1

Transport Mechanisms

On the upper shoreface it is generally accepted that – to a first approximation – cross-shore sediment transport is controlled by the balance between onshore transport oscillatory motions caused by incident wind waves and swell and offshore transport due to wave-generated mean currents. On the lower shoreface transport due to wave motions is still important, but mean currents generated mainly by tides and winds are also important (Seymour, 1980; Fewings et al., 2008). The orientation of these mean currents is typically alongshore, although significant on/offshore-oriented mean currents occur near the bed in situations with up/downwelling. Sediment transport rates are generally smaller on the lower shoreface than on the upper, as wave stirring of sediment is weaker. Focusing for the moment on the effect of wind waves and swell, a wave-cycle-averaged net transport is usually caused by an asymmetry in the velocity field, for example, caused by wave shoaling. During shoaling, wave and orbital velocity skewnesses develop such that the magnitude of onshoredirected orbital velocities become larger than offshore-directed orbital velocities and the duration of onshore flows becomes shorter than the duration of offshore flows. In the absence of further complicating factors (e.g., bedforms altering the phase relationship between flow and sediment suspension) this velocity skewness leads to a net onshore transport by wind waves, because sediment transport is a nonlinear function of fluid velocity. Velocity skewness has long been perceived as the major cause for net onshore wave-induced sediment transport (Wells, 1967). A theoretical example of the development of velocity skewness and sediment transport potential is illustrated in Figure 8. Wave shape and orbital velocity have been computed using second-order Stokes wave theory and assuming a wave height of 1 m and a wave period of 10 s. The sediment transport potential is calculated by assuming qpu3 (Bagnold, 1963; Bailard, 1981) and the lower panels illustrate transport potential integrated over wave crest and wave trough, respectively. As illustrated in Figure 8, when waves propagate into shallower water, the wave shape and the sediment transport potential become increasingly asymmetric and increasingly larger (wave-averaged) onshore sediment rates occur. Doering et al. (2001) found that a relationship exists between the magnitude of the wave orbital velocity skewness and the Ursell number, defined as: Ur ¼

HL2 h3

½12

where H is the wave height, L is the wavelength, and h is the water depth. If that is the case, then in theory it should be possible to predict the wave-induced sediment transport rate and direction from the Ursell number. However, it is well known that the net suspended sediment transport rate under skewed waves can be directed against the waves if the bed is covered by steep vortex ripples (Section 10.4.3). Bedforms induce phase lags between (orbital) velocity and sediment concentration through the ejection and subsequent convection of sediment-laden vortices at flow reversal (Vincent and Green, 1990; Doucette, 2000; van der Werf et al., 2007). Such phase lags are also a major reason why the direction of

Sediment Transport

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Figure 7 Laboratory measurements of ensemble-averaged sediment concentration at different elevations in and above the bed, plotted against wave phase t/T, where T is the wave period. The top panel shows horizontal fluid velocity with positive velocities directed onshore. Negative elevations are below initial bed level.

83

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Sediment Transport

h = 10 m

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Figure 8 (a) Theoretical wave orbital velocities computed from second-order Stokes wave theory for a wave height of 1 m and a wave period of 10 s at water depths of h ¼50, 10, and 5 m. (b) Shows sediment transport potential computed from q¼u3, and (c) shows total transport potential under wave crests and wave troughs for the three depths. Note that y-axis extremes are different for different water depths. Positive values are directed onshore.

suspended sediment transport is not uniform in the vertical, or why transport magnitude is not simply related to the magnitude of C. Figure 9 shows a set of illustrative measurements of suspended sediment transport profiles obtained by Vincent et al. (1991) during a minor storm event on the lower shoreface off Queensland Beach in Nova Scotia, Canada. The wave-induced transport was directed offshore very close to the bed at the beginning and end of the event when orbital velocities were relatively small, and ripples with a height 41 cm were believed to exist on the seabed. The wave-related transport reversed to onshore at higher elevations in the water column. During the maximum of the storm event, when ripples were likely washed out or small in amplitude, the wave-related transport was directed uniformly onshore in the vertical. Vincent et al. (1991) hypothesized that the shifting transport patterns were intimately related to changing bedform geometries, which in turn affected the phase relationships between u and C. When energy levels increase and bring about an increase in wave orbital velocity and bed shear stress, bedform steepness decreases and bedforms eventually disappear as the plane bed stage is initiated. This causes decreasing phase lags between u and C (Osborne and Greenwood, 1993). Detailed, large-scale laboratory experiments on such phase lags were reported for plane bed sheet flow conditions by Dohmen-Janssen et al. (2002). They found that phase lags scaled with z/wsT where z

is the elevation above the bed, ws is the sediment fall velocity, and T is the wave period. Thus, phase lags decrease with proximity to the bed, large grain sizes and long-wave periods (see also Figure 7). Orbital velocity skewness continues to increase as long as waves continue to shoal, but once the waves reach the upper shoreface and begin to break, the skewness decreases. Instead, a wave shape asymmetry develops that is expressed by a steep front face and a gently sloping rear of the wave; the wave form assumes a sawtooth shape, approximating a bore. Surf bores are associated with fluid acceleration skewness; large accelerations occur at the bore front and weaker decelerations occur after passage of the bore crest. Numerical models for sediment transport that rely exclusively on orbital velocity skewness as the only mechanism for onshore transport (e.g., Bailard, 1981; Marino-Tapia et al., 2007a,b) have tended to under-predict the onshore component of sediment transport. This has prompted researchers to search for alternative mechanisms for onshore sediment transport and Drake and Calantoni (2001) and Hsu and Hanes (2004) suggested that fluid acceleration skewness may be one such mechanism. Fluid acceleration is a useful means for quantifying the asymmetric nature of waves, encapsulating processes such as phase shifts of the bed shear stress relative to free-stream velocity (caused by the thin bottom boundary layer and thus large bed shear stresses under the front face of

Sediment Transport

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Figure 9 Record-averaged sediment transport profiles recorded by Vincent et al. (1991) on the lower shoreface of Queensland Beach, Nova Scotia using an acoustic backscatter system. The panels are arranged sequentially; the onset of the storm is represented by the upper panel and the end of the storm by the lower panel. Total transport is the sum of transports due to incident waves and mean currents, respectively. The wave contribution is highlighted with dark shading showing the onshore wave-related transport component, while light shading represents the offshore wave-related component. Adapted from Vincent, C.E., Hanes, D.M., Bowen, A.J., 1991. Acoustic measurements of suspended sand on the shoreface and the control of concentration by bed roughness. Marine Geology 96, 1–18.

waves), as well as pressure gradients into the bed (Austin et al., 2009). Predictions of observed, onshore oscillatory sediment flux using a Meyer-Peter/Mu¨ller type of model improved when fluid acceleration was included (Austin et al., 2009) and

85

Houser and Greenwood (2007) found large sediment suspension events correlated well with large fluid accelerations. In the surf zone, fluid acceleration may also be a proxy for breaker/bore turbulence (Puleo et al., 2003) since turbulence levels may be large and reach the bed at the front face of breaking waves, especially when the waves are plunging (Aagaard and Hughes, 2010). There appears little doubt that onshore, wave-induced transport is strongly related to asymmetries in the wave form, whether these are expressed through fluid velocity or fluid acceleration skewness. The significance of such skewness is likely to be more important for longperiod waves (and/or coarse grain sizes), because the sediment grains mobilized and transported onshore under the wave crest then have more time to settle (and/or settle more quickly) before velocity reversal. The foregoing discussion might suggest that sediment transport due to wind waves is always onshore directed. As the authors have touched upon earlier, this is not the case. Offshore wave-induced transport may occur if velocity skewness is negative and/or if bedforms (e.g., steep vortex ripples) shift the phase relationships between fluid velocity and sediment concentration by more than approximately 901, or because of bed slope. Strong wave/current interaction within the surf zone can also lead to larger amounts of sediment being mobilized on offshore wave strokes with a resulting offshore wave-related transport. Wave-induced transport may be either augmented or opposed by the transport due to mean currents. In Figure 9, for example, the wave-induced onshore transport is opposed by an offshore-directed mean transport caused by a quasi-steady mean current. On the lower shoreface, mean cross-shore transport may be caused by downwelling or upwelling flows due to onshore- or offshore-directed wind stress (Wright et al., 1991), tidal flows in cases when these are not oriented quite parallel with the shoreline (Houwman and Hoekstra, 1999), or Lagrangian Stokes drift. These types of flows are commonly relatively weak and waves are generally perceived as dominating the net cross-shore (onshore) sediment transport under nonbreaking wave conditions, for example, on the lower shoreface. Because beaches exist in the first place and because it is a general observation that they tend to accrete under nonbreaking wave conditions, this assumption makes intuitive sense. Although it is probably fair to say that the process assemblages and the relative strength of various transport processes are reasonably well known for the upper shoreface, such is not the case at intermediate (and large) water depths on the lower shoreface. Laboratory experiments conducted under more or less idealized conditions are generally inconclusive and only a few field experiments exist with an aim to document net long-term cross-shore sediment transport. Consequently, the cross-shore exchange of sediment between the lower and the upper shoreface is poorly known. Once waves start to break in the surf zone on the upper shoreface velocity skewness decreases and offshore-directed mean currents are enhanced significantly; the latter because of the shallow water depths and the added contribution to the offshore-directed return currents from wave breaking and surface rollers (Svendsen, 1984). Consequently, inside the breakpoint the mean (current-induced) transport may, in some cases, assume complete dominance leading to large, net

Sediment Transport

where qig, qinc, and qm are the sediment fluxes due to infragravity waves, incident waves and mean currents, respectively. In this formulation, qig expresses the relative contribution of oscillatory infragravity motions to total sediment flux. By way

of example QIG is plotted as a function of local water depth relative to water depth at the wave breakpoint, h/hb, for two beaches in Figure 10(a). Seaward of the wave breakpoint, oscillatory infragravity flux is mostly offshore directed, as expected, probably due to bound long-wave motions. Inside the wave breakpoint the importance of infragravity motions potentially increases approximately linearly, such that it may constitute about 70% of the total sediment flux near the shoreline. However, the transport can be either offshore-, or onshore-directed and it may also be negligible. Calculating the absolute magnitude of infragravity flux and plotting these data against distance to the wave breakpoint demonstrated a clear transport pattern. Landward of the breakpoint, infragravity transport was onshore, consistent 0.8 Dissipative beach Intermediate beach

0.6 0.4 0.2 Qig

offshore suspended sediment transport. As sediment concentrations are much larger on the upper than on the lower shoreface (Figures 2 and 6), mean currents on the upper shoreface are generally instrumental in creating large morphological changes during storms. Offshore-directed mean currents on the upper shoreface comprise both undertow and rip currents. When wave breaking is strong, both types of flows can attain large velocities, up to ca. 0.5 m s1 for undertows (Aagaard et al., 2005), and in excess of 1 m s1 for rip currents (Brander and Short, 2000). However, onshore-directed mean currents and mean transport may also occur on the upper shoreface, for example in cases when cell circulations exist in 3D morphological settings. Onshore-directed mean flows can develop across shallow bars between rip current channels, representing the onshoredirected limb of the circulation cell (Aagaard et al., 1998; 2006), and the speed of such onshore-directed rip feeder flows may be of the same order of magnitude as the offshoredirected rip current (MacMahan et al., 2005). Oscillatory flows due to infragravity waves are another significant mechanism for cross-shore suspended sediment transport in the nearshore. Contrasting reports have emerged on the relative importance and directional attributes of the infragravity-wave transport component. Seaward of the breakpoint, oscillatory infragravity transport typically constitutes only a minor fraction of the net transport and it is directed offshore (Ruessink et al., 1998). The reason for such a preferential direction of transport is tied to the occurrence of short wave groups and the bound infragravity waves forced by these groups. Groups of large wind/swell waves result in enhanced mobilization of sediment from the bed and this sediment is advected offshore by bound long-wave troughs that are phase-locked to the groups of large wind/swell waves (Shi and Larsen, 1984). Inside the (incident) wave breakpoint, infragravity motions are commonly standing in the cross-shore dimension. Net suspended-sediment transport rates due to oscillatory infragravity waves have been found negligible in some cases (Ruessink et al., 1998; Conley and Beach, 2003), and in other cases they dominate the total transport (Beach and Sternberg, 1991; Russell, 1993). In the inner surf zone of a dissipative beach, Houser and Greenwood (2007) found that infragravity sediment fluxes were large and their direction depended on the position of the wave breakpoint. When waves broke seaward of a bar crest the infragravity transport was directed onshore and forced an onshore migration of the bar. When waves broke landward of the bar crest the infragravity transport component was directed offshore. These conflicting reports on the role and significance of infragravity waves were partly reconciled by Aagaard and Greenwood (2008). They normalized the infragravity suspended sediment flux by the total sediment flux at a point, nominally located at 5 cm above the bed: qig QIG ¼   ½13 qig þ jqinc j þ jqm j

0.0

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86

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0

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0 x−xb (m)

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Figure 10 (a) The contribution from oscillatory infragravity waves to total suspended sediment flux, QIG (eqn [13]), plotted against local depth relative to water depth at the wave breakpoint, h/hb. The breakpoint is located at h/hb ¼1. (b) Infragravity oscillatory suspended sediment fluxes plotted against distance relative to the nearest breakpoint, x  xb. Positive values of x  xb indicate measurement positions landward of the breakpoint, and positive sediment fluxes are directed onshore. Data were collected at a dissipative beach (Skallingen, Denmark; circles) and at an intermediate-state beach (Staengehus, Denmark; crosses). Reproduced from Aagaard, T., Greenwood, B., 2008. Oscillatory infragravity wave contribution to surf zone sediment transport – the role of advection. Marine Geology 251, 1–14.

Sediment Transport

0.1 0.0 −0.1 −0.2 −0.3 0.5 0.0 −0.5 −1.0

Elevation MSL (m)

qx (kg m−2 s−1)

and erosion, respectively. A typical example is shown in Figure 11 from a double-barred beach where suspended sediment fluxes are plotted for both a high- and low-energy situation. In the former situation wave breaking occurred across both nearshore bars, whereas some wave reformation occurred in the troughs between the bars. In the latter situation wave breaking only occurred over the inner bar. In the high-energy case, the net suspended sediment fluxes were directed offshore at all measurement positions, except at the outermost station at the toe of the outer bar. The offshore sediment fluxes were caused by a dominance of the mean transport component caused by undertow. Sediment fluxes increased seaward and reached a maximum on the crest of the outer bar, and then decreased down the seaward slope of that bar. Such a transport pattern will generate a zone of erosion on the landward slope of the outer bar and a zone of accretion on the seaward slope, resulting in offshore bar migration. In the low-energy case sediment fluxes were directed mainly landward. Specifically, fluxes were landward directed at bar crests and seaward on the landward bar slopes. The onshore fluxes were driven by incident waves with positive orbitalvelocity skewness, and such a transport pattern generates erosion over the seaward slope of the bar and deposition on the landward slope causing an onshore bar migration. Note the much smaller observed transport rates during low-energy conditions, which is consistent with observations that morphological relaxation times are much longer under low-energy conditions compared to high-energy conditions. A similar spatial distribution of cross-shore transport was observed by Marino-Tapia et al. (2007a). Following Russell and Huntley (1999), they obtained a large number of velocity measurements from six different beaches and they calculated the third and fourth cross-shore velocity moments, which were used as proxies for bedload and suspended load

qx (kg m−2 s−1)

with Houser and Greenwood (2007), and decreased with distance from the breakpoint, while the opposite was true seaward of the breakpoint, with a cross-over in transport direction at the breakpoint (Figure 10(b)). Aagaard and Greenwood (2008) proposed that wave breaker zones constitute pick-up areas where large amounts of sediment are entrained and suspended in the water column, and that standing infragravity motions then act as an advection mechanism for moving sediment away from the breaker zone. Both the magnitude and direction of infragravity transport at a given position on the upper shoreface is determined by the relative position of the wave breaker zone. Under storm conditions, infragravity oscillations can become very large, particularly in the innermost surf zone. In such cases it has been shown that they may assume a dominant role in the suspension of sediment (Beach and Sternberg, 1988; Aagaard and Greenwood, 1995a). Oscillatory infragravity transport direction and magnitude may well then be a function of local infragravity velocity skewness rather than sediment pick-up in a breaker zone. The net suspended-sediment transport at any given position on the upper shoreface is generally regarded as the sum of the three transport components discussed above: (1) incident wind waves and swell that mainly, but not always, transport sediment onshore; (2) mean flows that mainly, but not always, transport sediment offshore, and (3) infragravity waves that commonly transport sediment in either direction. The largest transport rates occur in the bottom 50 or 100 mm of the water column (Conley and Beach, 2003) where sediment concentrations are large, an exception perhaps being in zones of plunging breakers where sediment is lifted to higher elevations (Yu et al., 1993). Furthermore, net sediment fluxes may be vertically segregated, with oscillatory (onshore directed) fluxes dominating in the very near-bed region where phase coupling between u(t) and c(t) is large, and mean fluxes dominating at larger elevations because of increasing current speed and decreasing phase coupling with distance from the boundary. This simplification ignores potential sediment transport processes such as Lagrangian mass transport due to Stokes drift and boundary layer streaming. Such processes are generally neglected, mainly because the former cannot be observed using stationary instruments and the latter is difficult to resolve. Boundary layer streaming causes weak mean currents that are confined to the bottom boundary layer and oriented in the direction of wave propagation, but they have not been positively identified in field measurements. This may be due to either the small vertical scales involved or because these currents are insignificant compared to other mean flows. Nevertheless, in a numerical modeling study Henderson et al. (2004) concluded that boundary layer streaming and Lagrangian mass transport may both be important and potentially contribute to onshore sediment transport and nearshore bar migration.

2 0 −2 −4 0

10.4.4.2

The Cross-Shore Distribution of Suspended Sediment Transport

The way that cross-shore sediment transport varies across the shoreface determines how the morphology changes. Spatially changing transport rates and directions set up transport convergences and divergences corresponding to zones of accretion

87

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Figure 11 Net cross-shore suspended sediment fluxes measured at 5 cm above the bed at an intermediate-state beach, Staengehus, Denmark. The upper panel shows fluxes during a low-energy situation and the middle panel is for a high-energy situation. The cross-shore profile is shown in the bottom panel for reference. Positive sediment fluxes were directed onshore.

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transport, respectively. The best-fit lines through the data points were termed transport shape functions and these shape functions showed that velocity moments were positive (due to positive orbital velocity skewness) in the wave shoaling regions seaward of wave breaker zones, indicative of net onshore transport, whereas velocity moments were negative (due to offshore-directed mean currents) through the majority of the surf zone, indicative of net offshore transport. These shape functions therefore predict erosion over much of the surf zone with sediment transport convergences in breaker zones, consistent with the patterns illustrated in Figure 11. The general form of the proposed shape function was confirmed qualitatively by Tinker et al. (2009) who measured suspended sediment transport directly instead of using velocity moment proxies, which formally assume proportionality between u(t) and c(t).

10.4.4.3

Cross-Shore Suspended Sediment Transport on Dissipative, Intermediate, and Reflective Beaches

Cross-shore sediment transport is qualitatively and quantitatively different on different types of beaches, because of the different history of wave transformation on each beach type (see Chapters 10.5 and 10.12, this volume). Dissipative beaches exhibit gentle cross-shore slopes, a relatively small vertical relief between nearshore bars and intervening troughs, and therefore (almost) continuous wave breaking through a wide surf zone. Breaking waves are mostly of the spilling type. Intermediate-state beaches possess steep, prominent bars with strong wave breaking, commonly of the plunging type and wave reformation in troughs (Wright and Short, 1984). Since wave set-up and undertow speed depend on the slope of the bed (Longuet-Higgins and Stewart, 1964; Longuet-Higgins, 1983; Aagaard et al., 2002), the mean current speed and hence the offshore-directed (mean) sediment transport component can be expected to be smaller, but extending over longer horizontal distances on dissipative beaches compared with intermediate-state beaches. On intermediate beaches strong undertows occur over bars with weak undertows in troughs. Moreover, suspended sediment loads will be locally large under plunging waves on intermediate beaches and small in troughs where wave breaking does not occur. In contrast, cross-shore gradients in sediment load tend to be smaller on dissipative beaches because turbulence from spilling breakers does not impact the bed to the same extent as turbulence from plunging waves. As a consequence, gradients in cross-shore suspended-sediment transport rates are expected to be larger on intermediate-state beaches than on dissipative beaches, causing the former to be more dynamic in terms of morphological change, which is in agreement with observations by Wright and Short (1984). Infragravity motions are generally more important to the net sediment transport on dissipative than on intermediate beaches, because of the continuous dissipation of incident wave energy and the concomitant growth of infragravity waves on the former. Figure 12 shows cross-shore velocity spectra and cospectra of sediment flux from the surf zone of a dissipative beach. Across the nearshore bar the oscillatory sediment

flux occurred mainly at incident wave frequencies, but as incident wind wave energy decayed over the bar, infragravity waves dominated the velocity field in the inner surf zone. The oscillatory sediment flux, displayed by the cospectra, occurred exclusively at low frequencies. Such infragravity-band, cospectral dominance is rarely seen on intermediate beaches where incident waves reform in troughs between bars. On such beaches, dissipation of incident wave energy is not as strong and the infragravity-wave flux tends to remain subordinate to sediment fluxes by incident waves. Direct field measurements of nearshore sediment transport on the shoreface of reflective beaches are lacking. On this beach type the lower shoreface extends to the wave breakpoint at the toe of the beach face and mean currents, such as undertows, are probably confined to a very narrow region near the foreshore and probably indistinguishable from swash flows. As waves are shoaling almost all the way to the beach it is to be expected that sediment transport will be dominated by wind/swell wave skewness, with a secondary offshore-directed contribution from bound infragravity waves. As wave skewness increases with decreasing water depth, and sediment stirring increases with increasing wave-orbital velocity toward the beach, onshore-directed sediment transport rates probably increase consistently toward the beach, potentially leading to a transfer of sand directly from the shoreface to the beach, again depending on the complications introduced by bedforms.

10.4.4.4

Sediment Transport in 3D Morphological Settings

The spatial distribution of cross-shore sediment transport described above strictly only applies when the morphology is homogeneous alongshore. In the shallow inner surf-zone the morphology is commonly rhythmic with crescentic or transverse bars interspersed with rip channels. The mean current circulation is then horizontally segregated, with strong offshore-directed rip currents in rip channels and weaker onshore-directed flows across the bar shoals completing the circulation cells (Haller et al., 2002). Due to the difficulties with installing instruments in an active rip current and the positional instability of rip channels, only a few studies have obtained measurements of sediment transport measurements in rips. Because rip current velocity depends on the intensity of incident wave dissipation across the shoals and the cross-sectional area of the rip channel that the return flow is forced through, rip velocity and related suspended sediment transport is typically tidally modulated, with maximum current speeds and offshore sediment transport rates occurring at low tide (Aagaard et al., 1997; Brander, 1999; MacMahan et al., 2005; Austin et al., 2010). When the rip current is most active at low tide, net sediment transport in rip channels is offshore directed because the mean (current-induced) transport component is dominant, but at high tide, or when waves are small, wave dissipation across bar shoals and ensuing rip velocity are weak and onshore transport due to incident wave velocity skewness may prevail. Suspended sediment transport across bar shoals in between rip channels is almost persistently onshore directed, perhaps due to acceleration skewness under breaking waves. The onshore-directed mean currents that are generated across

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Sediment Transport

Figure 12 Cross-shore velocity spectra (black, and left ordinate axis) and cospectra of cross-shore oscillatory sediment flux (blue, and right ordinate axis) at a dissipative beach. Note the progressive decrease in sediment flux at incident wave frequencies (f40.05 Hz) as the shoreline is approached, and the simultaneous increase in sediment flux at infragravity frequencies (fo0.05 Hz). The offshore significant wave height was 1.9 m and the mean water level was þ 0.9 m relative to mean sea level.

89

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the shoals and that feed the rip currents increase in strength with decreasing water depth because of more complete wave dissipation and depth confinement. Hence, the onshore transport at bar shoals is typically dominated by mean currents at low tide while oscillatory wave motions may dominate when water depths are larger at high tide (Aagaard et al., 1998, 2006) leading to onshore bar migration (Bruneau et al., 2009).

10.4.4.5

The Role of Bedload Transport

Previous sections have focussed on suspended sediment transport. There has been a long-standing debate concerning the relative significance of bedload versus suspended load. The debate has come about partly because of semantic difficulties: What exactly is bedload? In some cases, the distinction has been made on the basis of sensor location relative to the seabed, but a more rigorous definition was provided by Bagnold (see Section 10.4.1). The fact that bedload cannot yet be reliably measured in natural shoreface settings contributes to the uncertainty surrounding its importance. Based on sediment tracer measurements Komar (1978) argued that bedload contributes by far the largest fraction (75–90%) of the total longshore sediment transport. The argument was made that the tracer centroid in those experiments moved much more slowly than the mean current. Hanes (1988) later pointed out that these observations could be equally well explained by intermittent sediment suspension. Given the difficulties with measuring bedload reliably, techniques using bedform-tracking devices have been used on the assumption that bedform migration mirrors bedload transport (Hay and Bowen, 1993; Osborne and Vincent, 1993; Hoekstra et al., 2004; Maier and Hay, 2009). Dyer and Soulsby (1988) tracked migrating ripples to estimate bedload transport along with measurements of suspended sediment concentration and they found that for steady (tidal) currents on the lower shoreface of Start Bay, UK, bedload dominated immediately above the threshold velocity whereas suspended load was up to a factor of 17 times larger when flow velocities were strong. Styles and Glenn (2005) used a data-driven bottom boundary layer model to conclude that bedload on the midAtlantic shelf was more important than suspended load. On the upper shoreface and under strong wave action, Aagaard et al. (2001) used a bed-level sensor to track migrating megaripples and OBS-sensors were used for recording suspended sediment transport; the tentative conclusion was that bedload constituted 25% of the total sediment transport, with the remainder being transported in suspension. Other experimental work (Kobayashi et al., 2005; Kleinhans and Grasmeijer, 2006) and model tests (Li and Davies, 1996; Wenneker et al., 2011) have also suggested that suspended load is far more important than bedload under most conditions. When shear stresses become large bedforms are washed out and it is usually assumed, for example, based on Shieldsdiagrams, that suspended load becomes even more dominant than in situations when bedforms exist. This assumption is contradicted by the detailed large-scale laboratory experiments

by Dohmen-Janssen and Hanes (2002, 2005). Estimates of grain velocities were obtained in the sheet flow layer under flat bed conditions in a large wave flume using conductivity probes. The imposed fluid motions had large velocity skewness. Consistent with definitions, the top of the sheet flow/ bedload layer was selected as the level at which sediment concentration dropped below c ¼ 0.08 m3/m3, and based on this criterion, the observed sheet flow layer was in the order of 10 grain diameters thick and the experimental results indicated that on flat beds and in pure wave motion, bedload transport is about an order of magnitude larger than transport in suspension. However, the measured suspended sediment concentrations were 1–2 orders of magnitude smaller than what is typically observed in natural surf zones. The experimental evidence is thus highly contradictory on the issue of bedload relative to suspended load magnitude. Until reliable instruments for measuring bedload under natural conditions become available it is unlikely that the issue will be resolved. With regard to the processes driving nearshore bedload transport, orbital velocity skewness is a critical ingredient, because wave-induced bed shear stresses are larger than shear stresses generated by mean currents. Bedload transport is typically directed onshore (Styles and Glenn, 2005) consistent with onshore-directed orbital velocity skewness, and in situations when mean currents and net suspended sediment transport are directed offshore this offers an explanation for the often-observed cross-shore grain size segregation with a seaward-fining trend, since coarse grains are likely to travel in close vicinity to the bed and finer grain sizes higher in the water column (Vincent et al., 1983). In addition to velocity skewness, acceleration skewness may also be important to bedload transport. Hsu and Hanes (2004) and Calantoni and Puleo (2006) applied two-phase and discrete particle numerical models, respectively, to suggest that under sawtooth waves, horizontal pressure gradients generated by fluid acceleration contribute significantly to the net transport in the sheet flow layer, although they found that the effects were still subordinate to those of velocity skewness.

10.4.4.6

Numerical Models of Cross-Shore Sediment Transport and Beach Profile Change

Field and laboratory measurements of sediment transport have contributed vastly to our understanding of how beaches behave in nature. The question then is how well does the assimilation of this knowledge into numerical models quantitatively reproduce natural beach behavior? Many mathematical/numerical models for cross-shore sediment transport exist and these were typically validated using measurements of cross-shore profile change and applying the sediment conservation equation. One model frequently used by the scientific community is the energetics model which was originally formulated by Bagnold (1963) and later modified for wave-current flows by Bowen (1980) and Bailard (1981). The model relies on a velocity time series input, and it predicts bedload transport as a function of the third-order, near-bed, velocity moment and suspended transport as a function of the fourth-order

Sediment Transport

moment. Omitting the gravity terms that arise because of sloping seabeds and which are negligible in most applications, the model can be expressed as: iðtÞ ¼ rcf

  eb  es  juðtÞj2 uðtÞ þ rcf juðtÞj3 uðtÞ tan j ws

½14

where i(t) is the instantaneous immersed-weight sediment transport at the point where velocity measurements are made, u(t) is the instantaneous fluid velocity, r is the fluid density, cf is a drag coefficient analogous to a friction factor, eb and es are ‘efficiency factors’ for bedload and suspended load, respectively, f is the internal angle of friction, and ws is the sediment fall velocity. The model has been tested on numerous occasions, for example, using high-quality survey data from Duck, N.C., USA (Thornton et al., 1996; Gallagher et al., 1998; Marino-Tapia et al., 2007b). These tests all agree that the model works well under erosive conditions when the net sediment transport is directed offshore due to the undertow, but it cannot simulate profile development under fair-weather accretion conditions when sediment is driven onshore by the dominance of oscillatory wave motions (Voulgaris et al., 1998; Marino-Tapia et al., 2007b). With respect to the relative fraction of bedload and suspended load, model predictions in moderately or highly energetic situations indicate that suspended sediment transport is typically a factor of 3–5 larger than bedload transport, but any conclusions obviously depend on how well the model represents nature. The problems concerning a general underprediction of onshore wave-induced transport, and the fact that the energetics model does not specifically consider sediment concentration, but instead models sediment stirring/concentration implicitly through u2 and u3, have prompted researchers to propose more detailed numerical models and to consider additional mechanisms beyond (oscillatory) velocity skewness for onshore sediment transport. For example, Henderson et al. (2004) presented a wave phase-resolving model that includes sediment transport due to boundary layer streaming and Stokes drift (but excluding bedload and turbulence generated by breaking waves) and their tests of this model were promising since the model was able to simulate onshore sediment transport and ensuing landward bar migration at Duck. Similar results were obtained from an alternative phaseresolving model proposed by Hsu et al. (2006) that introduced different friction factors for waves and currents. A two-phase model developed specifically for sheet flow sediment transport, and driven by measured wave, current and turbulence information was proposed recently by Amoudry et al. (2008). This model calculates the Reynolds-averaged, 1D vertical mass and momentum equations of the separate fluid and sediment phases in order to predict suspended as well as high-concentration bedload transport. A later model-extension by Scott et al. (2009) included turbulence from breaking waves and tests in a large-scale laboratory experiment demonstrated an ability to reasonably predict instantaneous near-bed suspended-sediment concentration profiles, but the model could not simulate onshore sediment transport associated with observed landward bar migration and beach accretion. The reasons for the failure of the model were suggested to include nonlocal (onshore-directed)

91

advective sediment transport and nonlinear boundary layer streaming. Thus, a wide range of possible mechanisms has been tested to explain the onshore transport of sediment that must be involved in observed onshore bar migration during beach recovery. These mechanisms include velocity skewness, acceleration skewness, boundary layer streaming, Stokes drift, and turbulence generated by wave breaking. The conclusion must be that no single mechanism in isolation appears to be sufficient to fully account for observed and inferred onshore sediment transport on the upper shoreface. Research models for sediment transport have also found their way into engineering models for beach profile change. Examples include LITCROSS (STP; Fredsøe, 1993), CROSMOR (TRANSPOR; Van Rijn (2007)) and UNIBEST and its extension Xbeach (Roelvink and Stive, 1989; Ribberink and Al-Salem, 1995; Roelvink et al., 2009). These models are morphodynamic models in which a sediment transport module is included in looped computational schemes that also include input of offshore boundary conditions, wave transformation and nearshore profile change. A number of these morphodynamic models were tested by Van Rijn et al. (2003) against large-scale laboratory and field data sets. Reasonable simulations were obtained of beach response to storms (when mean currents (undertow) dominate the sediment transport and when the net transport is consequently directed offshore), but again the models were less successful during beach recovery phases and when longer time scales were considered, partly because of inadequate modeling of 3D phenomena in the inner surf zone. It is probably fair to conclude that our ability to quantitatively predict and model nearshore profile change through detailed cross-shore sediment-transport models is still some way into the future.

10.4.5

Longshore Sediment Transport

Longshore sediment transport rates are commonly considerably larger than cross-shore transport rates. In most cases, however, longshore transport gradients are much smaller than cross-shore gradients and hence the effect of longshore transport is generally more limited in influencing beach profile change along open beaches. Quantitative studies of longshore sediment transport have a much longer history than studies of cross-shore transport, partly because of the engineering need to solve siltation problems experienced at tidal inlets and harbor entrances. In contrast to cross-shore transport, longshore sediment transport is typically unidirectional over large spatial and temporal scales and the transport is mainly driven by mean currents. The longshore component of orbital velocity tends to be small on the upper shoreface, due to refraction of incident waves. Furthermore, in many cases, mean longshore currents are stronger than oscillatory cross-shore currents and hence exhibit proportionately larger transport rates. Consequently, longshore sediment transport due to wind waves can be considered negligible and this considerably simplifies the problem of identifying and separately quantifying the causative mechanisms. Incident wind/swell waves are perceived to provide the main part of the bed shear stress for mobilizing

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Sediment Transport

the sediment, which is then advected alongshore by quasisteady currents. The terms ‘longshore sediment transport’ and ‘littoral drift’ generally refer to the transport driven by wave-induced longshore currents on the upper shoreface. If the shoreline is straight and uninterrupted, then annual net alongshore transport can become very large; sometimes on the order of 106 m3 a1, for example, along the Danish North Sea coast. Historically, the amount of sediment transported along the coast (within the surf zone on the upper shoreface) has been related to the amount of energy available in the waves arriving at the wave breakpoint (Dean and Dalrymple, 2002), such that the volumetric transport rate can be determined by: Ql ¼

KECg sin ab cos ab KPl ¼ ðrs  rÞgð1  pÞ ðrs  rÞgð1  pÞ

½15

In this equation, which probably has its origin with the Los Angeles District of the US Army Corps of Engineers (Eaton, 1951), E is the wave-energy density, Cg is the wave group velocity, ab is the wave incidence angle at the breakpoint, rs is the sediment density, r is the fluid density, p is a correction factor for pore space, and K is a constant of proportionality. Instead of considering the processes actually driving the sediment transport, bed shear stress and longshore current speed are replaced by a proxy which is the longshore component of incident wave-energy flux. Much effort has been invested in trying to arrive at a single, optimum value of K. Early tests of eqn [15] relied mainly on field and laboratory measurements using tracer data, and/or sediment impoundment techniques. Later, streamer traps and vertical arrays of OBS were used. In a review of the then-available literature, Komar (1998) arrived at an optimum value of K¼ 0.70 when using the root-mean-square wave height in the expression of the longshore component of wave-energy flux. This was slightly lower than the K¼ 0.77 previously suggested by Komar and Inman (1970) on the basis of their pioneering tracer studies on two different California beaches. Instead of considering wave-energy flux, Inman and Bagnold (1963) developed a model based on the amount of power utilized by the flow to transport sediment and they arrived at an equation of the same form as eqn [15], but naturally with a different constant of proportionality. Using engineering quantities and assumptions about the relationship between longshore current magnitude and wave-energy flux, the Inman and Bagnold (1963) equation can be simplified to Ql pK 0 Hb2 V

½16

where V is the longshore current speed and Hb is the (significant) wave breaker height (see Kraus et al., 1982; Komar, 1998). Such a model is intuitively more appealing than that represented by eqn [15], because it explicitly considers the speed of the longshore current (and is not limited to longshore currents generated by wave breaking) and the bed shear stress is modeled through the squared wave height, which is proportional to the squared wave orbital-velocity. Field studies (Miller, 1999) have suggested that this equation may indeed be more reliable than the wave-energy flux approach. The formulation of Inman and Bagnold (1963) was

later extended by Bailard (1981) who integrated the instantaneous transport equations for bedload and suspended load to arrive at a set of equations involving the higher-order moments of orbital velocity. To arrive at a total longshore transport rate across the surf zone these equations need to be integrated across that distance. They have also been applied in the study of cross-shore transport (eqn [14]). Controversy has surrounded whether K (and K0 ) are really constants, or whether they depend on wave/sediment characteristics. Komar (1988) found no dependency of K on mean sediment grain size or beach slope, although this might have been expected unless the motion/suspension threshold was significantly exceeded for all grain sizes. Based on laboratory data, Kamphuis and Readshaw (1978) suggested that K varies with the Iribarren-number (i.e., beach slope, wave steepness and thus breaker type) and this was later supported through a literature survey that demonstrated a clear dependency of K on the Iribarren-number. Plunging/collapsing breakers result in larger K than spilling breakers (Bodge, 1989). Different studies have obtained K in the range 0.08–2.2 (Dean and Dalrymple, 2002). Based on impoundment studies, Dean et al. (1987) obtained K¼ 0.84–1.43, with a grain size dependency such that K increases with decreasing grain size, as expected. Wang et al. (1998) used streamer traps to measure longshore sediment transport on 29 low-energy beaches exhibiting a wide range of bathymetries (barred/nonbarred; steep/gently sloping) and a wide range of sediment grain size distributions (albeit all sandy beaches). They found that measured transport rates were an order of magnitude smaller than predicted by eqn [15] when using the recommended value of K. This study cast doubt on the practice of employing different measurement techniques to arrive at a singular value of K, and Wang et al. (1998) concluded that it is essential to reconcile the different measurement techniques of tracers, traps and short-term impoundments. By inference, it appears likely that one or more of these techniques is incapable of reliably measuring sediment transport. A comparative study, involving several measurement techniques, was undertaken by Tonk and Masselink (2005). From an intercomparison of longshore suspended-sediment transport measured simultaneously with streamer traps and with an array of OBS-sensors, they showed that the two techniques yielded similar transport rates. Through combination of the two techniques, the authors succeeded in obtaining longshore transport rates over large spatial and temporal scales. The calculated rates showed good agreement with the wave power approach and the recommended magnitude of K. It was evident that Ql is a strongly fluctuating quantity, however, which calls into question the approach of using short streamer trap deployments for making inferences about long-term, longshore transport rates. The large range of optimized calibration factors (K and K0 ) obtained on different types of beaches suggests that the variability may not only be due to measurement inaccuracies and partly flawed measurement techniques, but also due to important processes that are not accounted for in these approaches. Clearly, in order to obtain scientific understanding and more precise predictive capabilities of longshore sediment transport rates, such processes need to be identified. For example, Smith and Kraus (2007) stated that it is necessary to explicitly consider the oscillatory velocity component in shear

Sediment Transport

stress estimates for quantifying the amount of sediment mobilization. Furthermore, they demonstrated that much larger longshore transport rates occur for plunging breakers than for spilling breakers of the same wave height, which is consistent with the study of Tonk and Masselink (2005). A similar conclusion was reached by van Maanen et al. (2009) who tested the more detailed Bailard equation (eqn [14]) for suspended load. Using field measurements of suspended sediment concentration and fluid velocity in the shallow intertidal zone, they found that the Bailard model often underestimated observed longshore transport rates. Apart from potential experimental errors associated with the measurements of concentration using OBS-sensors, reasons for the underprediction were suggested to be a failure to account explicitly for wave breaking in the prediction of sediment mobilization. Despite inconclusive evidence, sediment grain size must also have an effect on longshore transport magnitude. The constants of proportionality in the longshore transport equations were derived for sandy beaches. In the case of coarser sediment fractions, mobilization thresholds should become increasingly important. For example, van Wellen et al. (2000) found that K-values on shingle beaches were much lower than standard values given in the literature for sandy beaches. Another plausible reason for the wide range of observed K-values relates to the fact that longshore transport in the surf zone cannot always be perceived as a ‘wave-stirring, current-transport’ mechanism. When longshore currents are strong, low-frequency (fE0.001–0.01 Hz) fluctuations of the current may develop. These fluctuations are superimposed on the steady current; they exhibit a meandering pattern alongshore and are termed shear waves, although they possess little or no surface expression. Current shear is strongest where the current is fast, and consequently, shear waves are often observed over nearshore bars and/or in the wave breaker zone. Since the sediment transport rate is generally considered dependent upon higher-order moments of velocity, fluctuations in longshore current speed (due to shear waves for example) might be expected to have a significant effect on longshore sediment transport rates and hence the magnitude of K. Aagaard and Greenwood (1995b) monitored longshore suspended sediment transport during a storm across a bar, and they reported that an average of 15% of the net (suspended) transport was due to shear waves and this transport was directed with the mean current. In a similar study conducted within the intertidal zone, Miles et al. (2002) found that shear waves contributed 12% to the longshore transport of sediment, but in this case the low-frequency oscillatory transport was directed opposite to the longshore current direction. The explanation for the contradictory transport directions probably rests with the phasing of suspension events relative to the oscillatory motions (Miles et al., 2002). Much effort has also gone into studying the cross-shore distribution of longshore sediment transport. Maximum transport rates tend to occur where waves are breaking and where energy dissipation is at a maximum. Since barred beaches commonly exhibit multiple zones of breaking located over successive bars, peaks in longshore transport are associated with bars, and lower transport rates occur in troughs.

93

A further transport maximum is generally located at the shorebreak close to the beach face (Bodge, 1989; Rosati et al., 1991). Seaward of the surf zone, longshore sediment transport driven by wave-generated currents rapidly drops off (Kraus and Dean, 1987). More sophisticated numerical models than eqns [15] and [16] exist for longshore sediment transport in the surf zone. Numerical models commonly use sediment diffusivity concepts (eqn [11]) to describe the mean and/or time-varying vertical distributions of suspended sediment concentrations, and bed concentrations are parameterized using mean or instantaneous bed shear stress (e.g., Rakha et al., 1997; Van Rijn (2007)). The magnitude and vertical distribution of sediment loads are then coupled to the vertical distribution of longshore current speeds. Reflecting the overwhelming dominance of studies on longshore sediment transport in the surf zone rather than on the lower shoreface, this section has so far covered only longshore transport driven by wave-induced currents. However, waves are capable of stirring sandy sediments at depths much larger than the wave breaker depth, and longshore transport also occurs on the lower shoreface where it is mainly driven by tidal and wind-induced currents. Since tidal currents are reversing, such transport is often considered to balance in the long term with negligible net transport of sediment. Observations of large bedforms (sand waves and sand ridges) on the lower shoreface (McBride and Moslow, 1991; Cacchione et al., 1994; van de Meene and van Rijn, 2000; Anthony and Leth, 2002) indicate that this is not always the case, however. Symmetric tidal flows augmented by wind driven currents can transport considerable amounts of sediment alongshore in the shoaling wave zone (Hequette et al., 2008). Field measurements by Cacchione et al. (1999) also indicated that large amounts of (fine) sand are transported at considerable depths along the California coast during storms. Figure 13 shows field measurements of suspended sediment transport at 8 m water depth on the lower shoreface off the Danish west coast. The reversing alongshore tidal currents are reflected in reversing sediment transport, but during energetic events, current speed and direction is strongly affected by the wind and sediment transport tends to be unidirectional for several tidal cycles. For this particular site, Aagaard et al. (2010) estimated an annual northward directed transport on the lower shoreface that was in the order of 105 m3 yr1, thus in some cases, longshore transport on the lower shoreface cannot be neglected.

10.4.6

Swash Zone Sediment Transport

Investigation of swash zone sediment transport, in terms of both experimental effort and knowledge, is still in its infancy compared with studies of the other nearshore environments. But the efforts have accelerated rapidly over the past 15 years. The approaches available to measure sediment transport in the swash are the same as those further offshore, but their application is more challenging due to the shallow and intermittent water depths. Early experimental studies used bedload traps, modified from those used in fluvial environments (Hardisty et al., 1984; Jago and Hardisty, 1984), as well as streamer traps

94

Sediment Transport

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Figure 13 Field measurements of (a) significant wave height, (b) mean water depth, (c) longshore mean current velocity, and (d) longshore suspended sediment transport in the lower 30 cm of the water column on the lower shoreface, off Vejers on the Danish North Sea coast. Reproduced from Aagaard, T., Kroon, A., Greenwood, B., Hughes, M., 2010. Observations of bar decay and the role of lower shoreface processes. Continental Shelf Research 30, 1497–1510.

to measure total load transport rates (Hughes et al., 1997a; Masselink and Hughes, 1998). On high energy, dissipative beaches with relatively deep, infragravity swash, OBS have been used to measure the suspension concentration and infer suspended load transport rates (e.g., Butt and Russell, 1999; Puleo et al., 2000; see also Section 10.4.2). The ultimate goal of modeling sediment transport rates is generally to predict morphological change, which is the result of spatial gradients in net sediment transport. Recent experimental methodology has attempted to resolve the critical net transport gradients more directly by measuring rapid bed elevation changes across the beach profile (Baldock et al., 2005; Masselink et al., 2009; Blenkinsopp et al., 2011). The current state of the art with respect to sediment transport modeling has not advanced far beyond ad hoc modifications to equations initially developed for steady flows. Implicit in these is the assumption that the sediment transport rate is in equilibrium with the local forcing; i.e., the bed shear stress. The usual approach uses the horizontal flow

velocity and a friction factor to obtain the bed shear stress (eqn [6]). Most observations of the local horizontal flow velocity over a swash event are consistent with the following pattern in an Eulerian reference-frame (Figure 14): peak velocity in the landward direction occurring at the start of the swash event when the shoreline arrives at the measurement location; decelerating flow toward the time of flow reversal; an acceleration of the flow following flow reversal in a seaward direction; and finally the peak velocity in the seaward direction occurring near the end of the swash event, marked when the shoreline recedes past the measurement location. The duration of the uprush is typically shorter than the backwash, thus the velocity skewness is directed offshore (Masselink and Russell, 2006), although this is not necessarily the case and depends on a swash boundary condition in a way that is still not yet fully understood (Guard and Baldock, 2007; Power et al., 2011). Even under modest wave conditions, peak flow velocities routinely reach 1–2 m s1, and up to 3 m s1 on the steepest beaches where swash is driven by a

Sediment Transport

where q is the immersed-weight sediment transport per unit width of beach integrated over the half-swash cycle of interest (uprush or backwash), u is the mean flow velocity during the half-swash cycle, t is the duration of the uprush or backwash, tan j is the friction angle of the sediment, and tan b is the beach gradient. In the case of the uprush, tan b is positive and in the case of the backwash it is negative. The parameter k is an empirical coefficient. Theoretically, it represents friction effects in relation to the bed shear stress as well as the Bagnold’s transport efficiency factor. The Meyer-Peter and Mu¨ller sediment transport equation, modified for the swash, can be written as (Hughes et al., 1997a)

X (m)

30 ADV location

25

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0.1

0 Cor. (%)

100 50

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u (m s−1)

0

++ + ++++++++++++ ++++++++++++++++ ++ ++++++++++++++++++++ ++ ++ +++ ++ + ++ ++++ + +++++++++++++++++++ ++++++++++++++

1 0 −1 1 0 −1 460

462

464

466

468

470

t (s) Figure 14 Example of a single swash event showing (from top to bottom): time series of the shoreline position X (with location of the Acoustic Doppler Velocimeter (ADV) used to measure flow velocity marked); the local swash depth h; the signal correlation (Cor., solid line) and signal-to-noise ratio (SNR, crosses) of the ADV signal used as indicators of data quality; the unprocessed horizontal velocity record u (solid line); and the processed record (open circles). The vertical dashed lines through the bottom three panels delimit reliable ADV data. Note that in the bottom panel, the flow velocity is undefined when the beach is ‘dry’. Reproduced from Hughes, M.G., Baldock, T.E., 2004. Eulerian flow velocities in the swash zone: field data and model predictions. Journal of Geophysical Research 109, C08009, doi: 10.1029/2003JC002213, with permission from American Geophysical Union.

shore-breaker (Masselink and Hughes, 1998; Butt and Russell, 1999; Hughes and Baldock, 2004; Masselink and Russell, 2006). Bed shear stresses and sediment transport loads are, therefore, large in the swash zone. Near-bed suspended sediment concentrations can reach 100–200 kg m3 (e.g., Osborne and Rooker, 1999; Butt and Russell, 1999; Puleo et al., 2000; Masselink et al., 2005; Miles et al., 2006), and the total immersed mass transported in a half-swash cycle can reach several tens of kg m1 beach width (Hughes et al., 1997a; Masselink and Hughes, 1998). Two equilibrium-type sediment transport equations that have been applied to the swash are those initially developed by Bagnold (1963; 1966) and Meyer-Peter and Mu¨ller (1948). The Bagnold sediment transport equation, modified for application to the swash zone, can be written as (e.g., Hardisty et al., 1984) q¼

ku3 t tan j7tan b

95

½17

F ¼ kðy  yc Þ3=2

½18

where F is the dimensionless sediment transport over a halfswash cycle, y is the Shields parameter (eqn [9]) in which the bed shear stress t (eqn [6]) is calculated based on the peak flow velocity, and yc is the critical Shields parameter required for sediment motion. The parameter k is again effectively a calibration coefficient accounting for a range of physical processes not explicit in the model (see below). Masselink and Hughes (1998) also provide formulations of these two models (eqns [17] and [18]) based on instantaneous flow velocities. Several studies have tested the accuracy of the models against field measurements and some examples are listed in Table 1. There appears to be little in the way of consistency in the calibration coefficient k for either the modified Bagnold or Meyer-Peter–Mu¨ller transport equations (Table 1). This probably reflects the fact that each of the studies has measured different modes of sediment transport – either bedload, suspended load, or total load. Rather than an explanation, this further highlights inconsistencies. For example, the modified Bagnold model is for bedload, so one might expect the k-value in studies measuring total load would be larger than those measuring bedload only, but the reverse appears to be the case (Table 1). Similarly, in the case of the modified MeyerPeter–Mu¨ller equation, one would not expect k-values between those studies measuring total load and those measuring suspended load only to be so similar (Table 1). These inconsistencies are at least in part due to the inherent errors in measurements of sediment transport, flow velocity, and the methods used to estimate bed shear stress. It has been recognized for some time, however, that there are other relevant factors that are not yet fully understood or included in the current generation of sediment transport models. What is consistent across the studies listed in Table 1 is that the calibration coefficient for the uprush is significantly larger than the backwash (with the exception of Hardisty et al., 1984). Comparing the measured suspended sediment concentration over a typical swash cycle with that expected from an equilibrium-type transport model (i.e., concentration proportional to the velocity-cubed) confirms the general impression that processes not accounted for in this model type make sediment transport during the uprush appear more effective than the backwash (Figure 15); particularly given that the velocity skewness is directed offshore (e.g., Hughes and Baldock, 2004; Masselink and Russell, 2006). Unaccounted for processes that have been proposed include: (1) settling lag; (2) advection of bore-suspended sediment; (3) unsteady and

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Sediment Transport

Table 1 List of studies testing eqns [17] and [18] against field data Model and study (Modified) Bagnold Hardisty et al. (1984) – bedload Hughes et al. (1997a, b) – total load Masselink and Hughes (1998) – total load Masselink et al. (2009) – total load (Modified) Meyer-Peter–Mu¨ller Masselink and Hughes (1998) – total load Masselink et al. (2005) – suspended load

k-up

k-back

k-up (inst.)

k-back (inst.)

tan b

D50 (mm)

70 13.4 25.9 –

70 – 14.4 –

– – 14.5 9.0

– – 7.4 6.5

0.03–0.05 0.12 0.14 0.06

0.23–0.66 0.3 0.5 0.4

19.9 16.4

8.9 11.3

– –

– –

0.14 0.015–0.025

0.5 0.27–0.29

Also listed are the calibration coefficients for each study, reduced to a common dimensional form (kg m  3) in the case of the Bagnold equation and a common nondimensional form in the case of the Meyer-Peter Mu¨ller equation. For the Bagnold equation either the mean flow velocity over the half-swash cycle or instantaneous flow velocities were used. In the case of the Meyer-Peter Mu¨ller equation, the peak flow velocity was used. Source: Data from Hardisty, J., Collier, J., Hamilton, D., 1984. A calibration of the Bagnold beach equation. Marine Geology 61, 95–101; Hughes, M.G., Masselink, G., Brander, R.W., 1997a. Flow velocity and sediment transport in the swash zone of a steep beach. Marine Geology 138, 91–103; Hughes, M.G., Masselink, G., Hanslow, D., Mitchell, D., 1997b. Towards a better understanding of swash zone sediment transport. Proceedings Coastal Dynamics. ASCE, New York, pp. 804–823; Masselink, G., Hughes, M.G., 1998. Field investigation of sediment transport in the swash zone. Continental Shelf Research 18, 1179–1199; Masselink, G., Russell, P., Turner, I., Blenkinsopp, C., 2009. Net sediment transport and morphological change in the swash zone of a high-energy sandy beach from swash event to tidal cycle time scales. Marine Geology 267, 18–35, and Masselink, G., Evans, D., Hughes, M.G., Russell, P., 2005. Suspended sediment transport in the swash zone of a dissipative beach. Marine Geology 216, 169–189.

1

1

0.75

0.75

0.5

X

X

0.1 0.5 0.05 0.25

0 (a)

0

0.25

0.25

0.5 t

0.75

0

1 (b)

0

0.25

0.5 t

0.75

1

0

Figure 15 (a) Measured normalized suspended sediment concentration mapped onto the x–t plane. Concentration was normalized against the maximum observed value in the data set, and x and t were normalized against the maximum runup length and swash period. (b) Predicted suspended sediment concentration on the basis of a transport model of the form q¼f(u3). Reproduced from Hughes, M.G., Aagaard, T., Baldock, T.E., 2007. Suspended sediment in the swash zone: heuristic analysis of spatial and temporal variations in concentration. Journal of Coastal Research 23, 1345–1354, with permission from Coastal Education and Research Foundation.

nonuniform flow; (4) turbulence; and (5) vertical flow through the bed (Hughes et al., 1997a, b, 2007; Masselink and Hughes, 1998; Turner and Masselink, 1998; Butt et al., 2001, 2004; Masselink and Puleo, 2006). Despite the assumption inherent in eqns [17] and [18] that the sediment transport rate is in equilibrium with the bed shear stress, in reality this cannot be true, particularly for the suspended load component since it takes a finite time for sediment to settle to the bed. In decelerating flow during the uprush, this settling lag will have the effect of more sediment being transported than expected under equilibrium conditions, thus requiring a greater calibration coefficient for the uprush compared with the backwash in eqns [17] and [18]. This effect may be enhanced by hindered settling due to turbulence (Nielsen, 1992) or the presence of high sediment concentrations. A 50% reduction in the settling velocity of sediment with high suspended sediment concentrations has been demonstrated for swash flows (Baldock et al., 2004).

Using a nonlinear shallow water model to describe the swash hydrodynamics, Pritchard and Hogg (2005) showed that settling lag can overcome offshore-directed velocity skewness and produce net transport in the onshore direction. Advection of presuspended sediment from the bore front and the bore collapse zone would also increase the sediment transport rate in the uprush above that expected from the local bed shear stress alone. The ability of the bore to deliver sediment into the swash depends on the concentration carried by the bore as well as the volume flow that the bore delivers. The former is probably related to the bore strength and the intensity of any interaction with the preceding backwash (Puleo et al., 2000; Butt et al., 2004; Hughes et al., 2007). The latter has been investigated in the laboratory and it appears that fluid from a distance of up to half of the swash length behind the bore front is advected into the swash zone, and approximately 25% of the sediment carried by the bore can reach the midswash zone (Baldock et al., 2008; Alsina et al., 2009).

Sediment Transport

Vertical velocity gradients in the bottom boundary layer of the swash seem to be greater during the uprush compared with the backwash; the most likely explanation being the unsteady nature of the flow (Cowen et al., 2003; Raubenheimer et al., 2004; Masselink et al., 2005). Larger velocity gradients mean that there will be larger bed shear stresses for a given free-stream flow velocity during the uprush, thus requiring a larger calibration coefficient for the uprush in eqns [17] and [18]. Furthermore, during the uprush, the flow is decelerating so the flow velocity responsible for entraining sediment will always be larger than that associated with the sediment in transport, while the opposite is true in the backwash. This advection lag also works to make the transport during the uprush appear more efficient than equilibrium concepts would predict (Hughes et al., 2007; Pritchard, 2009). Turbulence in the swash zone is locally generated at the bed throughout the swash cycle due to shear, and is also generated at the free-surface and advected into the region during bore collapse (Yeh and Ghazali, 1988; Petti and Longo, 2001). The net result is that the uprush is more turbulent than the backwash, particularly in the region near the bore collapse point (Hughes et al., 2007). Consequently, larger bed shear stresses will occur during the uprush than expected from the horizontal flow velocity alone (Aagaard and Hughes, 2006). This, together with a lower settling velocity for suspended sediment due to the turbulence, would enhance the sediment transport efficiency of the uprush over that expected from the equilibrium transport models. The final unaccounted for process in the energetic-based transport models that has been recognized is the effects of vertical flow through the bed. These effects may increase the apparent efficiency of the uprush over the backwash in two ways. First, infiltration of the swash flow into the beach can lead to thinning of the boundary layer and bringing faster velocities closer to the bed, hence greater bed shear stresses and sediment transport for a given free-stream flow velocity. Second, downward seepage through the bed may have a stabilizing effect due to drag on the sediment grains and an increase in their effective weight (Turner and Masselink, 1998; Baldock et al., 2001). Groundwater exfiltration has the reverse effect in both cases. Using field data and a modified sediment transport model, Butt et al. (2001) argued that boundary layer thinning/thickening will dominate on beaches where the sediment size is greater than 0.4–0.6 mm, and seepage effects will dominate for smaller grain sizes. The effects seem small for sandy beaches compared with likely measurement errors; an apparent difference in the uprush transport of 10% and backwash transport of 4.5% (Butt et al., 2001). Based on morphodynamic evidence, others have argued that infiltration effects on sediment transport are insignificant for sandy beaches (Weir et al., 2006). It seems likely that the effect on sediment transport from vertical flow through the bed will be best developed on gravel and coarser beaches where the backwash discharge can be reduced by up to 50% due to infiltration of the uprush (Austin and Masselink, 2006). Efforts have been made to increase the sophistication and accuracy of eqns [17] and [18] by modifying them to address some of the issues just discussed. For example, the unsteady nature of the flow has been addressed through inclusion of a

97

term describing landward-directed flow acceleration (Nielsen, 2002; Puleo et al., 2003), but this appears to be important in only a very localized region close to the bore collapse point, with acceleration over the majority of the swash zone being always directed seaward (Hughes and Baldock, 2004; Pritchard and Hogg, 2005; Baldock and Hughes, 2006). Aagaard and Hughes (2006) attempted to account for some turbulence effects by using a bed shear stress formulation that more explicitly includes the Reynolds stresses, rather than adopting the usual assumptions associated with a formulation based on the horizontal flow. They achieved some improvement in predictive skill, as did Butt et al. (2004) by including boregenerated turbulence into the energetic-based equations. Notwithstanding these efforts, however, a usable sediment transport model that includes all of the important physical processes recognized above is still some way off. All available formulations require calibration for the beach and wave conditions of interest, as well as the position of interest in the swash zone (Aagaard and Hughes, 2006). It is still a matter for debate as to what proportions of sediment transport occur as bedload versus suspended load in the swash. It is generally acknowledged that both occur, and some suggest a separation between the half-cycles: predominantly suspended load during the uprush and bedload during the backwash (Horn and Mason, 1994; Masselink and Puleo, 2006). It is clear that transport occurs at high shear stress levels, as indicated by the calibration coefficients for eqn [18], which are generally larger than the usual value of 8–12 (Table 1; cf. Nielsen, 1992). The Wilson (1987) criterion for sediment transport as sheet flow (y40.8) is typically satisfied in the swash zone (Hughes et al., 1997b; Masselink and Hughes, 1998). By most definitions, sheet flow includes both bedload and suspended load transport modes, albeit the suspended load generally stays very close to the bed. There is again debate as to which transport mode will dominate sheet flow. Arguments based on Bagnold (1966) would suggest predominantly suspended load, whereas arguments based on Wilson (1987) or Nielsen (1992) would suggest bedload (see Hughes et al., 1997a for discussion). Putting semantics aside for the moment, it certainly becomes easier to obtain high temporal-resolution measurements of sediment transport as one moves away from the bed, thus the detailed nature of suspended sediment transport has been a focus of many recent studies. As suggested above, however, there is no clear understanding of how representative this is of the total load transported. The vertical distribution of suspended sediment in the nearshore zone commonly conforms to an exponential profile, and this appears to also be true for the swash zone (Miles et al., 2006). In this case, the concentration Cz at elevation z above the bed is Cz ¼ Co ez=ls

½19

where Co is a reference concentration at the bottom of the vertical profile representative of the mobile bed, and ls is a mixing length scale defined as the ratio of the sediment diffusivity to the settling velocity of the sediment. Some measured values of reference concentrations and mixing lengths inferred from fitting eqn [19] to field data are listed in Table 2. Both variables are larger for the uprush than the backwash, which is consistent with the general observation that suspended

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Sediment Transport

Table 2 List of reference concentrations and mixing lengths measured in the swash zone on two beaches of contrasting beach slope and grain size Site

Co

ls

130 71

0.039 0.023

188 42

0.05 0.04

255.3 172.3

0.06 0.068

a

Perranporth Uprush Backwash Perranporthb Uprush Backwash Sennenb Uprush Backwash

tan b

D50 (mm)

0.015–0.025

0.27–0.29

0.032

0.24

0.084

0.58

a

Data from Masselink, G., Evans, D., Hughes, M.G., Russell, P., 2005. Suspended sediment transport in the swash zone of a dissipative beach. Marine Geology 216, 169–189. b Data from Miles, J., Butt, T., Russell, P., 2006. Swash zone sediment dynamics: a comparison of a dissipative and an intermediate beach. Marine Geology 231, 181–200.

sediment concentrations are largest during the uprush, and also that the sediment is mixed higher up into the water column. The latter is probably due to the greater turbulence intensities already described for the uprush as well as the greater accommodation space (or depth). The two variables are not steady, but rather they change with time during a swash event. Available observations from a single beach show that the reference concentration is maximum at the start and end of the swash event, whereas the mixing length is largest at the start of the uprush, falls off rapidly and then remains relatively constant over the remainder of the swash cycle (Masselink et al., 2005). Figure 16 depicts a useful summary of sediment transport under free (noninteracting) swashes. The generally negatively skewed velocity time series is shown, together with the generally deeper uprush compared with the backwash. The earliest stages of the uprush and the latest stages of the backwash are shown associated with the deepest mobilization of the bed and the greatest transport, consistent with the largest flow velocities and bed shear stresses at these times. Turbulence intensity is greater and vertical mixing is larger in the uprush than in the backwash. Sheet flow transport is shown associated with the times of largest flow velocity and bed shear stress, whereas bedload is shown dominating either side of flow reversal. Around the time of flow reversal, the water column can be clear of sediment. The boundary layer decay and growth with time for the uprush and backwash, respectively, are also shown and they highlight the importance of the unsteady nature of the flow. Most of the studies summarized to this point have sought to minimize the complexity of the problem by hand-selecting swash events that are largely free from interaction with preceding swashes or following waves; so called free swash (Hughes and Moseley, 2007). Most existing hydrodynamic models for swash are only suited to this situation (e.g., Pritchard and Hogg, 2005; Guard and Baldock, 2007), and as we have seen, existing sediment transport models are certainly not up to dealing with the complexities of interacting swash. The region of the swash zone that is dominated by free swash may be nearly 100% on steep beaches, but is usually well

below 50% on gently sloping beaches (Hughes and Moseley, 2007). So despite having learnt a great deal about the nature of sediment transport under free swash, it is uncertain how helpful this will be to predicting morphological change on the beach if it represents significantly less than the whole picture of the swash zone. Moving forward, the nature of swash interactions and their influence on sediment transport as well as the connection between the swash zone and inner surf zone are critical areas for investigation. A partial response to these complexities is the use of sediment-transport shape functions, which largely circumvent the difficulties of wave–swash interactions and coupling with the inner surf zone. Shape functions describe the net sediment flux as a function of the independent variable distance, or some variable that has a consistent behavior with distance, usually in the cross-shore direction. Early shape functions involved measuring the moments of flow velocity across the surf and swash zones and then deriving the net sediment-transport function through application of energetics-based transport models (e.g., Russell and Huntley, 1999; Masselink, 2003). However, these suffer from the shortcomings described earlier for equilibrium-type transport models. More recently, measurements of the net sediment fluxes have been used to derive the shape function, either from coincident measurements of flow velocity and suspended sediment concentration (Butt et al., 2002; Aagaard and Hughes, 2006; Tinker et al., 2009), or from measurements of bed elevation change and applying the principle of mass conservation (Weir et al., 2006; Masselink et al., 2009). The independent variable in sediment-transport shape functions is often scaled to be dimensionless with the intention that the shape function can be applied to a variety of beaches. To date, a shape function from one beach has not been applied to another, however, and it seems unlikely that such an exercise would be successful given the degrees of freedom associated with shape functions. For example, Weir et al. (2006) described four different shape functions for berm morphodynamics alone. Considerably more field measurements are required to determine if there is a relatively manageable set of unique shape functions that account for most of the morphodynamic behaviors one seeks to model. Even then, predicting the correct rate of morphological change will almost certainly still require tuning of the shape functions for each situation. Net sediment fluxes over a single or a group of swash events can be very large (up to 100 kg m1 beach width (Masselink et al., 2009)). Nevertheless, to maintain a stable beach slope the sediment transported landward by the uprush must be balanced by that transported seaward by the backwash when averaged over a relatively small number of swash cycles. On a natural beach, individual random swashes begin at different points on the beach face, run up to different elevations, and interact to a lesser or greater extent with preceding or subsequent waves at different locations on the beach face. While sediment transport by free swashes are an important part of beach morphodynamics, dealing with sediment transport in the presence of random interacting swash is clearly equally important. When incoming bores are traveling over an existing swash lens, there are landward-directed flow accelerations, horizontal pressure gradients, and injections of near-bed turbulent kinetic energy with the passage of each bore front

Swash velocity

Sediment Transport

99

Uprush 0 Backwash

Top boundary layer Turbulence Sediment settling Infiltration Exfiltration Immobile bed Swash depth

Sheet flow layer

Dry bed

Sediment suspension

Suspension + sheet flow

Settling + bed load

At rest

Bed load

Suspension + bed load

Sheet flow + suspension

Dry bed

Figure 16 Schematic of the sediment transport process during a swash event, free from interaction with preceding or following waves; in an Eulerian reference frame. Reproduced from Masselink, G., Puleo, J., 2006. Swash zone morphodynamics. Continental Shelf Research 26, 661–680.

(Puleo et al., 2003; Butt et al., 2004). These can significantly enhance sediment mobilization (Calantoni and Puleo, 2006). Similarly, when strong backwash flows arrest the passage of the next incoming wave in a hydraulic jump, the large vertical flow velocities can also enhance sediment mobilization (Butt and Russell, 2005). Whether a beach face erodes or accretes probably has as much to do with the net transport direction under interacting swash as it does with that under free swashes. The degree to which wave–swash interactions are influencing sediment transport on the beach face must be reflected in the ratio of the wave period in the inner surf zone (Tis) to the swash period (Ts). If Tis/Tso1, there should be considerable wave–swash interactions on the beach face (cf. Kemp, 1975). Under increasing wave-energy conditions, the wave spectrum generally becomes more broad-banded leading to increased wave–swash interaction, and Kemp (1975) showed that these conditions lead to offshore sediment transport. If the net sediment transport direction is offshore on the lower beach face where swash interactions are most common, and hence there is no sediment advection to the upper beach, then velocity skewness on the upper beach

where free swashes are most common would ensure that offshore sediment transport occurs across the entire swash zone, thus causing beach erosion (Hughes and Moseley, 2007). Alternatively, if the net sediment transport direction is onshore on the lower beach face, then advection of sediment onto the upper beach face could overcome the offshoredirected velocity skewness, thus resulting in beach accretion (Hughes and Moseley, 2007). The next generation of swash zone sediment-transport models almost certainly requires capability to describe interacting and free swash to correctly predict the exchange of sediment between the lower and upper beach face. As an extension to Figure 16, Figure 17 presents a conceptual description of sediment transport in a natural swash zone consisting of random interacting swashes in a Lagrangian reference-frame. An incoming bore is shown in panel (a), carrying suspended sediment toward the beach face where the preceding swash cycle has fully completed. In panel (b), the incoming bore has collapsed and the swash lens is moving up the beach carrying residual turbulence and sediment from the incoming bore, as well as sediment locally entrained in the

100

Sediment Transport

Interacting swashes

Interacting swashes

Free swashes

(a)

(d)

(b)

(e)

(c)

(f)

Free swashes

Figure 17 Schematic of the sediment transport process during a swash cycle that includes interaction with following waves during the uprush and backwash; in a Lagrangian reference frame. The lengths of straight arrows indicate relative flow velocity, short curved arrows indicate turbulence or vertical flow, and gray dots indicate suspended sediment. The zone of wave-swash interactions is characterized by positive and negative flow accelerations and potentially positive or negative velocity skewness, whereas the zone of free swash is characterized by only negative accelerations and skewness.

swash zone. The flow throughout the uprush is decelerating and most of the sediment is shown being carried by the swash tip, where the bed shear stresses and turbulence are greatest (Barnes et al., 2009). Panel (c) shows a following bore moving up the beach and interacting with the existing swash lens while it is still climbing the beach. The modified flow field due to the second bore is shown enhancing sediment mobilization in the interior of the underlying swash lens. In panel (d), the swash is shown having almost reached its runup length and the internal flow is approaching reversal. In this example, the flow is shown as being relatively clear, but the entire suspended sediment load need not necessarily settle before the backwash commences. The backwash is shown accelerating down the beach face in panel (e), picking up sediment from the bed as it progresses. In panel (f), another bore is shown approaching the beach before the preceding backwash is complete. The opposing horizontal flows and the vertical flow associated with the hydraulic jump

enhance the sediment load carried by the next bore, increasing the sediment that will be carried by the next swash cycle, irrespective of the fact that its runup length will probably be relatively modest due to the energy dissipation in the hydraulic jump. To summarize, the zone of wave–swash interactions is characterized by positive and negative flow accelerations and potentially positive or negative velocity skewness, whereas the zone of free swash is characterized by only negative accelerations and skewness. The advective exchange of turbulence and sediment between these two parts of the swash zone are critical to morphodynamic modeling. A variety of alternative interaction scenarios could have been presented in Figure 17, and the point is that random interacting swash will likely confound the modeling efforts long after the complexities of sediment transport by free swash have been solved.

Sediment Transport

10.4.7

Concluding Remarks

This chapter has summarized the current state of the art in our understanding of nearshore sediment transport, specifically in wave-dominated settings composed of sandy sediment. The knowledge base in this particular area of geomorphology is large, yet many gaps remain. The subject area continues to be the focus of a dynamic research effort by geomorphologists, as well as engineers and oceanographers. There are many questions at the fundamental level that remain to be resolved; for example, the relative contributions of bedload and suspended load transport across the nearshore zone. Bed shear stress continues to be the preferred parameter for predicting sediment transport processes, but the most appropriate means for quantifying and accounting for all the important contributors is still evolving. These and similar issues are important to our fundamental understanding of sediment transport, but the solving of all these alone will probably not provide the predictive capability required by geomorphologists to understand and model coastal morphodynamics. There remain many research problems to explore at the broader system level. For example, the impact of short- and long-wave interactions on sediment transport gradients and morphology. Parametric models and numerical models have been commonly used to explore issues at this level, but systems analysis techniques might offer significant advances in the near future. Research into nearshore sediment transport will continue for some time yet and will benefit greatly from ongoing development on several fronts: for example, technological improvements in instrumentation, integration of in situ instrumentation with remote sensing techniques that can provide the system-scale context, and advances in computational efficiency, to name a few.

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Biographical Sketch Troels Aagaard is an associate professor in physical geography at the Institute of Geography and Geology, University of Copenhagen, Denmark where he obtained his PhD in Coastal Geomorphology in 1990 and a DSc in 2003. He held an NSERC International Fellowship in 1991–92 to conduct postdoctoral research on coastal sediment transport at the University of Toronto and was head of the Coastal, Estuarine, and Marine Research Group at the Institute of Geography, U. Copenhagen in 2004–06. He received the Niels Nielsen award from the Royal Danish Geographical Society in 1993. His main research interests are coastal processes, morphodynamics, and sediment transport, and he has published about 80 papers on these topics. Through his career, he has collaborated with scientists from, and on beaches in, Denmark, Canada, Australia, New Zealand, the Netherlands, and the UK.

Michael Hughes completed his PhD at the Coastal Studies Unit, University of Sydney investigating wave runup on beaches. Since then, he has worked in both academia and government research agencies. Michael has maintained his initial research interests in beach and surf zone morphodynamics, but also enjoyed opportunities that broadened his research experience to include most marine environments; from coastal estuaries and beaches, across the shelf to ocean basins. This experience includes investigating cohesive sediment dynamics in estuaries and deltas, quantifying seabed dynamics in the vicinity of sand banks occupying shallow seaways, characterizing physical aspects of benthic habitats, and modeling physical disturbance as an ecological factor in determining marine biodiversity.