Coarse sediment particle motion under highly asymmetrical waves with implications for swash zone sediment transport

Coastal Engineering 71 (2013) 60–67

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Coarse sediment particle motion under highly asymmetrical waves with implications for swash zone sediment transport Ahmad Shanehsazzadeh a,⁎, Patrick Holmes b a b

University of Isfahan, Isfahan 81746-73441, Iran Imperial College of Science and Technology, London, SW7, United Kingdom

a r t i c l e

i n f o

Article history: Received 27 April 2012 Received in revised form 7 August 2012 Accepted 9 August 2012 Available online 30 August 2012 Keywords: Sediment transport Swash zone Asymmetric wave Experiment Particle jump length Coarse sediment

a b s t r a c t Hydrodynamics and sediment transport in the swash zone are unique and very complex phenomena. Acquiring a robust model for predicting sediment motion in the swash zone requires in-depth insight about the behavior of sediment particles in highly asymmetric and turbulent waves that continuingly uprush the beach face and retrieve in backwashes. In order to consider a physical system of the coarse particle motion in the swash zone with a reduced number of external parameters and capture some of the realism of the situation, the experiments are conducted in rather simple conditions to provide some information about the particle responses in terms of jump length against asymmetric waves to be implicated for the swash zone. The results show that despite reduction of many external parameters, jump length is still a highly skewed stochastic parameter. The probability distribution of jump length is quite wide (large variance) and skewed, different from that of saltation length in steady unidirectional flow, in which the distribution is close to normal. Considering integral of excess energy of an arbitrary single wave over its duration as a rational and meaningful represen
 tative of flow condition, the average jump length JL incremental trends reduces in the higher energy condition, resulting in a linear trend in logarithmic scale. The JLs due to higher turbulent kinetic energy follow similar trend of less turbulent flow conditions. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Sediment transport is the key process in the coastal zone that shapes the beach profile and coastline evolution. One of the dynamic parts of a beach is the swash zone i.e. the part of a beach that is frequently covered by uprushes and exposed by return of water seaward. Processes in the swash zone have direct impact on sediment transport and overall morphological evolution of coastline. In addition, the swash zone is the boundary condition for the integrated domain of models of the coastal zone and therefore, better knowledge of the processes involved in the swash zone has a significant influence on the overall accuracy of the predictions of those models (Longo et al., 2002). Nevertheless, hydrodynamics and sediment transport in the swash zone are still the challenging subject for scientists and coastal engineers. Acute unsteadiness, non-uniformity and high turbulence of the flow in the swash zone, in addition to the phenomena of in/exfiltration and, more importantly discontinuity of the flow, are unique features of the swash zone (Bakhtyar et al., 2009; Butt et al., 2001; Elfrink and Baldock, 2002). Although remarkable improvements have been achieved in understanding the physics and the processes involved in the swash zone, ⁎ Corresponding author. Tel.: +98 311 7934525; fax: +98 311 793 2089. E-mail addresses: [email protected] (A. Shanehsazzadeh), [email protected] (P. Holmes). 0378-3839/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.coastaleng.2012.08.003

our knowledge about the swash zone, particularly sediment transport in the swash zone is not adequate for engineering applications and requires significant advances (Puleo and Butt, 2006). This is even more critical for coarse sands and gravel beaches in bed load or sheet flow mode of transport (Pedrozo-Acuña et al., 2007). Several improvements are still needed before a general, robust, and reliable mathematical model of the swash zone transport is obtained (Larson et al., 2004). One of the basic issues in this regard is behavior of sediment particles within the swash zone. In other words, it shall be further investigated on how sediment grains are mobilized and transported in the swash zone. There are many such small‐scaled investigations about the particle behavior under unidirectional flows and some in oscillatory condition; however, within the swash zone it is rare. Nevertheless, to achieve the realistic model for the problem of sediment transport in the swash zone, such in-depth understanding is vital. Indeed, sediment transport in the swash zone is the result of the action of a sequence of swash events quite different from the surf zone and beyond (Masselink and Puleo, 2006). When a wave breaks and an event sweeps the swash zone, the flow carries some amount of particles landward from each section of the beach face due to uprush and conversely some amount seaward due to backwash. The number of particles in motion and their destinations depends on the characteristics of the swash events. Three modes of transport namely suspension load, bed load, and sheet flow are expected in the swash zone; however, for coarse particles the former is not occurred.

A. Shanehsazzadeh, P. Holmes / Coastal Engineering 71 (2013) 60–67 1.4

Horizontal velocity (m/s)

3 2

Velocity(m/s)

61

1 0 -1

1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4

-2

9

10

11

12

13

14

15

Time (s) -3 528

530

532

534

Fig. 3. Velocity time-histories of the waves generated by Single Asymmetric Wave Generator, SAWG.

Time(s) Fig. 1. Field measurement of a swash event (Shanehsazzadeh and Holmes, 2007).

2. Experiments

Among the important features of the flow in the swash zone is being highly asymmetric (Shanehsazzadeh and Holmes, 2007). The velocity skewness in the uprush is directed offshore (see Fig. 1). In the backwash there is uncertainty due to emerging of the velocity meter due to thin lens of retrieving water. Numerical models of swash hydrodynamics also predict offshore skewness in the swash zone (Pritchard and Hogg, 2005). The acceleration skewness has direct effect on the rate of sediment transport (Nielsen, 2006). In order to get insight into the grain motion in the swash zone, and to provide data for developing conceptual models (such as Shanehsazzadeh and Holmes, 2010) or validation of numerical models in this regard (e.g. Calantoni et al., 2006; Hoque and Asano, 2002), one solution might be reducing the number of influencing parameters to appreciate the effect of each parameter, separately. Considering this concept, the present study investigates one directional particle motion under highly asymmetric waves using laboratory tests. Moreover, the behavior under less and highly turbulent are compared. For this purpose, the bed load mode of transport of coarse sediment is considered in terms of particle jump length in response to the flow regime fairly similar to what is experienced in the swash zone. Three modes of transport namely suspension load, bed load, and sheet flow are expected in the swash zone; however, for coarse particles the former is not occurred. Obviously, the flow regimes produced in this study are not fully identical with what is experienced in the swash zone, yet they contain one of the most important characteristics of the flow in the swash zone which is asymmetry. Hence, the study is valuable in providing understanding of particle response in bed load mode of transport at this flow condition. The laboratory experiment has been briefly presented in Shanehsazzadeh and Holmes (2010) in application of data for a conceptual model and this paper describes more details of the tests and interpretation of the data which are required for comparative applications.

Damper

Paddle

In order to generate a single, very highly accelerated asymmetric wave in the laboratory, similar to the flow over the surf and swash zone, a mechanical apparatus called Single Asymmetric Wave Generator (SAWG) was designed and constructed. Fig. 2 shows a sketch of the apparatus. A traveling carriage mounted on the sides of a long flume of 10 m length and 0.3 m width, moves a paddle very rapidly through initially still water in the flume and thus generates a single wave. The motive power of the carriage is provided by falling weights through a pulley system. As can be seen in the figure, the carriage is connected to the weight by the cables through the power transfer system, via pulleys on axle A. A buffer arrests the carriage before it hits the main transfer axle A. In addition, a damper of very flexible rubber avoids the heavy impact on the buffer which would cause unwanted disturbances in the velocity profile. Fig. 3 shows a number of the near bed water velocity time-histories of the unbroken waves generated by SAWG. It should be noted that in this stage the experiments of particle motion are mostly conducted within water. Furthermore, the apparatus at this stage is designed to generate uprush and as shown in Fig. 3, backwashes are absorbed. Nevertheless, the generated waves being highly accelerated and skewed is very close in behavior to the flow regime in the swash zone and elucidate some aspects of sediment transport in that area. According to the field data measured at number of beaches (Shanehsazzadeh and Holmes, 2007), the average maximum velocity and time laps of uprushes are in order of 1.5 m/s and 2.5 s, respectively, depending on slope and wave characteristics. Therefore, the amounts of maximum velocities of generated single waves are fairly representatives of real swash velocities. Repeatability is an important consideration when the same condition must be reproduced in an experiment several times. As the sediment particles behave randomly in identical flows, the nature of the experiment in this study demanded the extensive repetition of the same experiment. Thus, the system was tested to ensure repeatability. In order to increase the range of the jump length data for more energetic conditions, two flow conditions were also selected from the

Carriage

Flume Buffer

0 10 20 30 40 50 60 70 80

Weight

Pad

Fig. 2. The sketch of the Single Asymmetric Wave Generator (SAWG) apparatus.

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Table 2 Solitary wave characteristics.

Velocity (m/s)

1.2 1 0.8

Flow condition

Vmax (m/s)

T (second)

θ maxa

0.6

1 kg 2 kg 4 kg 6 kg 8 kg 10 kg 14 kg

0.64 0.68 0.80 0.87 0.98 1.04 1.09

1.70 1.60 1.68 1.52 1.16 1.00 0.80

0.145 0.163 0.203 0.242 0.332 0.392 0.472

0.4 0.2 0 -0.2 -0.4 10

12

14

16

18

20

Time (s)

a

θ ¼ τ0 =ðρs −ρÞ gd50 in which τ0 is bed shear stress.

Fig. 4. Velocity time history after breaking.

SAWG. Jump length in this context means the difference between the new and original positions of the particles due to the unidirectional single waves. However, due to the coarse size of the particle, the particles mostly experience just one saltation at the interval of studied flow. In all conditions the water depth was kept constant (100 mm) and the bed was horizontal with about 30 mm thickness. The bed thickness is enough for the experimented flow range; erosion being always less than the provided thickness. Table 2 presents the maximum velocities and durations of each event (T), and maximum flow intensity (Θmax) as defined in the table note, for the selected time-histories of Fig. 2. For calculation of Θ, bed shear stress is considered for waves, according to Soulsby (1997) and Nielsen (2002), in which wave friction factor is determined from the ration between the actual length traveled by the water in the wave motion and bed roughness. In the table and hereafter, each time-history is characterized by the weight which was used in the SAWG to produce that time-history (see Fig. 2). Although video filming is commonly used to investigate the detailed motion of grains in flows (Gallagher et al., 1991; Hu and Hui, 1996a; Lee et al., 2000), due to requirement of repeating the experiment several times (more than 200 times for each flow condition) to get average jump length, extraction of the data from the video films would be very tedious and time-consuming. Therefore, in this study the jump lengths of particles were measured by eye sighting. For the monitoring of the jump length of particles by eye, between 12 and 14 of the grains of the bed were painted with different colors in order to distinguish them from the others. Then the original and new positions of each one were recorded before and after each wave event, respectively. As depicted in Table 2, the amounts of flow intensity, Θ, are mostly about and greater than 0.2, thus according to the literature (Hu and Hui, 1996a) majority of particle motion is expected to be in saltation mode. This is also observed in the present experiment. As the particles were firstly dropped on the surface, it is anticipated that the results would be different from the condition in which the particles naturally lay inside the surface. From a physical standpoint, the grains on the surface experience larger forces due to their greater exposure and are subject to less hindrance from the neighboring particles. Fig. 6 shows the average of the jump lengths in some flow regimes. The solid circles are the result of the first runs when the particles

region after breaking. For this purpose the depth of water was decreased from 100 mm to 25 mm by means of a gradual slope from the top of which a horizontal bed with depth of 25 mm was provided. The generated waves broke on the slope and then propagate as a bore in a very shallow water condition, providing higher velocities of up to 1.4 m/s as well as longer durations as shown in Fig. 4. On the other hand, owing to the breaking and also the shallow water, the flow contains massive turbulence close to the bed. The jump lengths (JL) of well-rounded, very narrow banded particles of d50 = 3 mm were measured in various velocity profiles of solitary waves, provided by the SAWG. The particle specifications of the grain are presented in Table 1. The velocity time-history of water was measured by a laboratory Acoustic Doppler Velocitimeter (ADV), with the rate of sampling being 25 Hz. In the context of sediment transport, the velocity just outside the boundary layer would be a reasonable choice for a representative velocity. Fig. 5 shows the vertical profile of horizontal velocity for two representative asymmetric single waves generated in the laboratory by SAWG. As can be seen in the figure, except within the area very close to the bed (boundary layer) i.e. a depth less than about 10 mm, the velocities are almost constant up to the still water level, above which the velocity increases substantially. Thus, according to the vertical profiles of velocity, a distance between 12 and 15 mm from the bed was chosen as the position for the velocity measurement, which, on average, corresponds to a position just outside (the edge of) the boundary layer (van Rijn, 1993). For the measurement of jump length, seven flow conditions were selected from numerous possible asymmetric waves generated by the Table 1 Grain particle specifications. d50 = 3 mm Almost spherical to well rounded ρs = 2.55 gm/ml = 2550 kg/m3 Ws = 0.29 − 0.33 m/s 0.39

160

160

140

140

120

120

Depth(mm)

Depth(mm)

Size Shape Density Fall velocity Porosity

100 SWL 80 60

100 SWL 80 60

40

40

20

20 0

0 0

0.5

Velocity(m/s)

1

1.5

0

0.5

1

Velocity(m/s)

Fig. 5. Vertical profile of maximum horizontal velocity for two single waves generated by SAWG.

1.5

A. Shanehsazzadeh, P. Holmes / Coastal Engineering 71 (2013) 60–67

when the energy of the wave increases, the weight of density migrates from near zero to greater values. The results on the distribution of jump lengths obtained in this study provide unique and interesting information from a micro-scale view point of the sediment transport process in response to asymmetric waves. However, in the present study, as the first stage, hereafter the
 average jump length JL is considered for discussion. Later, the distribution of jump lengths could be used to allocate various destinations of particles according to their corresponding densities (or percentage) in a probability distribution. As stated in Table 1, all particles under investigation were from the well-rounded category, however they can still be visually classified as well-rounded, very well rounded and almost spherical. Considering fall velocity as a general indicator of the shape of particles; the more rounded particles having greater fall velocity, experiment shows that the jump length of the spherical particles is less than that of the less rounded shapes (results are not shown). It can be interpreted in a way that the process of motion here includes mostly jumping rather than rolling, where the less-rounded particles provide greater traction forces at the beginning of the takeoff; hence, greater roundness, which is an advantage for rolling is of less importance in saltation.

First runs 80

Second runs 60

40

20

0.6

0.7

0.8

0.9

1

1.1

Maximum velocity (m/s) Fig. 6. The average jump length (JL) of the first and second runs of SAWG.

were dropped on the surface, and the hollow circles are of the second ones, when the particles had already been mixed with the bed sediment grains due to the first runs. It appears that the first jump lengths are approximately two times greater than the second ones. Then, the jump lengths were measured in some successive runs (third, fourth, etc.). No significant differences were observed between the JL of the second and the consecutive runs, meaning that the jump lengths in the second runs can be considered as the natural behavior of the particles in the bed surface.

3.1. The representative parameter of single asymmetric waves Introducing a logical parameter (or parameters) representing all behavior and characteristics of the flow over the bed, with regard to sediment transport, has been the matter of extensive investigation. In the case of currents, the problem is rather simpler, but in oscillatory flows and particularly asymmetric, skewed waves, it is difficult to introduce a single, deterministic parameter representing all influencing factors in the process. In oscillatory flow, the velocity changes in time and therefore the flow parameter to apply for sediment transport is also a function of time. Moreover, the vertical profile of horizontal velocity always changes temporarily and spatially in a very complex manner (Foster et al., 2000). Soulsby (1997) applied maximum velocity as the representative for estimate of bed load rate of a half wave cycle. In his formulation the instantaneous sediment transport rate from the steady formula of Nielsen (1992), with quadratic based shear stress, has been integrated over a half 2nd order Stokes wave and presented in terms of umax. Ribberink (1998) on the other hand used the average shear stress for a half wave of sinusoidal and 2nd order waves. Both considered a particular oscillatory wave pattern to derive the representative flow parameter in their formulations. For the case of an arbitrary shape of near bed velocity time-history, however, the question still remains to be answered as to what parameter of the flow would be the more appropriate one?

3. Experimental results Fig. 7 shows the distribution of jump lengths for a selected number of asymmetric waves under investigation. Each graph corresponds to the flow condition which has been characterized by the weight used in the SAWG apparatus to produce that time-history (see Fig. 2 and Table 1). 6kgS corresponds to the flow after breaking and in very shallow water conditions, as described before, where the velocities are higher with more fluctuations and the events are longer in duration (Fig. 4). The number
 of measured jump lengths (sample), the average jump length JL and standard deviation (SD) are shown in each graph.
It should be mentioned that in calculating the average jump  length JL , the zero jump lengths were also included. As can be seen in the figure the jump lengths display a wide range from zero up to 400 mm in some cases, with large standard deviations. This indicates the sensitivity of particles to their location within the neighboring particles and to the flow (the only variable in the experiments and, of course, an unavoidable one). It also appears from Fig. 7 that the distributions are very skewed toward zero JL. However,

6kgS

10kg

0.2

0.2

0.12

JL (mm)

Fig. 7. Distribution of jump lengths (JL) due to action of single asymmetric waves (SD denotes Standard Deviation).

250

225

200

175

100

400

350

300

250

200

0 150

0 100

0.04

50

0.04

75

0.08

50

Frequency

0.08

0

Frequency

0.12

JL (mm)

No=277 Average = 58mm SD= 57 mm

0.16

150

No.=77 Average = 115mm SD= 105 mm

0.16

125

0.5

0

0 0.4

25

Average jump length (mm)

100

63

64

A. Shanehsazzadeh, P. Holmes / Coastal Engineering 71 (2013) 60–67

In order to determine a rational parameter, representing all or most of the important characteristics of an asymmetric wave with regard to sediment transport, one can start from the approach of Bagnold, in which the motion of sediment particles is ascribed to the energy of water. The general definition of work done can be expressed as follows: Useful work ¼ e  available energy:

ð1Þ

In Eq. (1) for the case of sediment transport, useful work is sediment motion, e is an efficiency factor and available energy is in fact the power of the flow. The available energy can be conceptually converted to excess energy, as part of the total available energy is spent to overcome the stabilizing forces. In a single wave event, which can be generally considered as an arbitrary near bed velocity time-history, it is more appropriate to apply the equation for the entire wave, i.e. to integrate the excess energy over the time interval of the single one directional wave and then attribute it to the particle responses. Useful work here is the process of sediment transport for a single wave with duration of the period of the single wave, T. For the case of coarse particles in bed load mode of transport W can be defined as (Shanehsazzadeh, 2004): W ¼ w tanα

N X

JLi ¼ w tanα ⋅N⋅JL

ð2Þ

i¼1

in which: w α N JL

individual weight of particles Dynamic friction angle Number of particles in motion Average jump length of particles.

The process of sediment transport in a single wave motion is converted to the product of the number of particles in motion and their average jump lengths, multiplied by a constant. The excess energy of water in time interval T of the single wave event is defined as: T

E ¼ ∫ ðτ0 −τ cr Þuðt Þdt

ð3Þ

0

in which:

Shear stress in the highly accelerated velocity time-history of the swash zone has recently been a controversial subject (Nielsen, 2006). With application of the quadratic relationship between shear stress and near bed velocity, Eq. (3) is converted to:   1 1 2 2 ρf w uðt Þ − ρf w ucr uðt Þdt: 2 2 0

ð6Þ

N⋅JL∝σ:

The parameter sigma introduced here can be considered as a rational and meaningful parameter of single asymmetric waves with arbitrary near bed velocity time histories. In the parameter sigma, u(t) is considered velocity time history just outside of the boundary layer (van Rijn, 1993) which is also the case in the calculation of ucr. Threshold velocity ucr in parameter sigma for such particular flow condition is a matter of noticeable arguments. Validity of existing formula introduced for rather different flow condition of unidirectional or sinusoidal waves (for instant in Kolahdoozan et al., 2011; Komar and Miller, 1974; van Rijn, 1993; You, 2000) must be taken with precaution. For the case of 3 mm particles the results are scattered in the references from 0.36 to 0.52 m/s. In this study, ucr = 0.45 m/s is used which is approximately average of the various methods and is also relevant to the outcome of present data corresponding to almost zero JL. 3.2. The relationship between JL and flow parameter σ Fig. 8 presents the relationship between dimensionless parameter of JL/D, D being the particle diameter, and the flow parameter σ, Eq. (5), in logarithmic scale for the flow conditions of Figs. 3 and 4. Two black diamonds in the figure are corresponding to the after breaking test results from more energetic and turbulent flow conditions of 2kgS and 6kgS. These two pieces of data have been separated from the others because of the relatively different flow regimes, with longer period and highly fluctuated velocity time history as shown in Fig. 4; which are more similar to the swash zone. The linear trend line in the logarithmic scale indicates that, the jump length is decreased when the flow intensity is increased. It shows similar trend to the saltation of particles in unidirectional flow, in which it was found by Lee et al. (2000) that under a strong flow condition, the average saltation length of particles is only a function of the particle size and shape and has nothing to do with the flow condition. Two data of more energetic and turbulent flow conditions, more or less follow the trend of the other data of relatively non-fluctuating conditions. This indicates that turbulent kinetic energy which transferred to the bed does not increase the jump length. This is in contrast to the conclusion of the literature on influence of turbulent kinetic energy due to bore collapse on sediment transport in the swash zone in suspension mode of transport (Butt et al., 2004; Puleo et al., 2000). 3.3. JL on slope

The near bed shear stress (N/m 2), The critical shear stress at threshold (N/m 2), Time-history of near bed velocity (m/s).

τ0 τcr u(t)

value of the inside when it is not negative. Therefore, from Eqs. (1), (2) and (5), JL and N are proportional to sigma i.e.:

Sediment transport in the swash zone in reality takes place on a sloping beach; however, the results expressed so far are for horizontal beds. It is now important to further investigate the influence of slope

100

T

ð4Þ

R2 = 0.9554

JL/D

E¼∫

10

Now, if parameter sigma is introduced as follows: σ¼

 1 T  2 2 ∫ b uðt Þ −ucr > uðt Þdðt Þ: 3 0 ucr

ð5Þ

Then, the excess energy of water, E would be proportional to sigma. Sign b….> in Eq. (5) is called singularity function and defined as being zero when the inside the angle brackets is negative and is the

1 0.1

1

10

100

Sigma Fig. 8. JL−σ relationship. Black diamonds represent highly fluctuated flow conditions.

A. Shanehsazzadeh, P. Holmes / Coastal Engineering 71 (2013) 60–67

on the sediment motion. For this purpose a limited set of experiments were conducted on a 10% up-slope. No significant discrepancies were recognized between the JL on the 10% up-slope and the trend of the others on a horizontal bed (Shanehsazzadeh, 2004). It can be concluded (at this stage) that the slope does not considerably affect the average jump length due to an asymmetric skewed solitary wave. It should be noted that the modification of threshold velocity on slop (Soulsby, 1997) is not applied in calculation of sigma.

65

length of particles in saltation can be taken as independent statistical parameters from the conditions of flow and sediment and that they follow a Γ-distribution (a skewed distribution), but very close to a Gaussian distribution. However, the distribution of jump length due to single asymmetric waves as can be seen in Fig. 7, is different, showing fundamental differences in their behavior compared to that in unidirectional flow. As can be seen in the figure, the jump lengths display a wide range with large standard deviations and fully dependent on flow intensity.

4. Discussion 4.1. Jump length distribution

4.2. Acceleration and inertia force

As can be seen in Fig. 7, the response of particles to a single asymmetric wave is a random phenomenon similar to the saltation of particles in a unidirectional flow. It is well documented that the motion of sediment particle in bed load is a stochastic phenomenon. Flow characteristics including near bed velocity (shear stress) fluctuation due to turbulence as well as particle characteristic namely particle shape and position are influencing factors that result in such complex stochastic behavior (Cheng et al., 2003a, 2003b; Van Rijn, 1993; Zanke, 2003). By assuming a probability distribution function for the grain shear stress and particle position among the other particles in terms of angle of repose, the distribution function of bed particle instability or initiation of motion are analytically derived by Zanke, 2003. However, such theoretical study for particle jump length is not found in the literature. Instead for saltation of particles in unidirectional flow, Hu and Hui (1996b) and Lee et al. (2000) through an experimental study found that, the dimensionless saltation length, height and velocity of particles follow a distribution close to Gaussian distribution function, independent from the conditions of water and sediment at least for energetic flows. Nevertheless, the comparison between the particle jump lengths due to a solitary wave and continues saltation of particles in unidirectional flow is mostly valid in terms of the kinematics of the motion, i.e. similarity in the pattern of particle motion in the flow. In terms of the kinetics of particles, which involves the effective forces on the particles and elements of the equation of motion, there are some basic differences. The saltation of particles in unidirectional flow is due to a constant effect of destabilizing forces including drag, lift and in some cases inertia (van Rijn, 1984). On the other hand, in the transport of particles due to a single wave the particles move under the action of variable forces over a limited time interval within an event. Also, the bouncing behavior of saltation does not necessarily appear in the jump length concept. In addition to this basic difference, there are also differences in the forces that act on the particles. The inertia force arising from fluid acceleration in asymmetric waves could have a considerable influence on the jump length (Nielsen, 2002). In contrast, when the particles are at rest, they need additional energy for mobilization, or in other words, an extra force is necessary to accelerate particles from zero to a certain velocity in the direction of flow. This situation is also common in oscillatory flows (Fredsoe and Rasmussen, 1980); the friction factor, relating bed shear stress of flow and particle parameters, for particles at rest (static friction factor) is different from that for particles in motion (dynamic friction factor). This means that the friction force could be higher for a single wave, where the particles start moving from rest, compared to a condition in which particles move almost continuously in direction of flow. It can be conceptually concluded that despite the apparent similarity between jump length due to asymmetric waves and the saltation process in currents, the results of one are not interchangeable with the other. Hu and Hui (1996a, 1996b) studied the stochastic characteristics of bed load transport in unidirectional flow regimes via the measurement of saltation of particles using advanced high-speed photographic techniques. They found that the probability density distribution of

The asymmetric wave generated in this study, similar to what is experienced in the swash zone is highly accelerated (Shanehsazzadeh and Holmes, 2007). In unsteady flow, the bed load transportation may differ from that in steady flow because of the inertia of the sediment grains moving as bed load (Baldock and Holmes, 1997; Fredsoe, 1993). Therefore, there is an expectation that inertia force arising from this acceleration could have a considerable influence on the jump length. However, in introducing flow parameter, sigma, the acceleration effects are overlooked. Table 3 shows the maximum on-shore (positive) acceleration of the flow in m/s 2 in waves under investigation in the present study (Figs. 3 and 4). As the energy of flow is increased, the acceleration is also increased. This trend brings an expectation that in the strong conditions like 2kgS and 6kgS with considerable inertia forces, there must be a greater jump length, compared to the condition in which the inertia forces are not taken into consideration. However, it can be seen in Fig. 8 (the position of two black diamonds, corresponding to 2kgS and 6kgS), the acceleration does not have a significant influence on JL (at least in the flow range of this study). A numerical analysis of drag and inertia forces for limited timevarying flow conditions showed that (the results are not presented) the inertia forces are much greater than drag forces (up to 300%), but only at the early stage of the velocity time-history. As the flow velocities approach the threshold of motion and higher, the ratio of inertia to drag forces reduces to 8%. This means that at the time when the particles are in motion or about to move, the inertia forces are not active; they are relatively high initially but they are unable to dislodge the particles. The conclusion made here on the influence of acceleration is tentative. Since, in the last two flow conditions the turbulence density is also high and might contradict the effect of inertia force due to acceleration. Clearly, more experimental and analytical studies are necessary to elucidate the influences of acceleration on particle motion. It can be, for instance, investigated through comparison of the particle response to two events having equal sigma, but with different shapes of velocity time history, i.e. different acceleration. Considering acceleration being less influential on particle response, leads to the assumption that in the swash zone, with putting aside other factors, particles behave similarly in backwash and uprush, despite that this two events are different in terms of acceleration.

Table 3 Maximum on shore acceleration of flow. Flow condition

Acceleration (m/s2)

1 kg 2 kg 4 kg 6 kg 8 kg 10 kg 14 kg 2kgS 6kgS

2.17 3.00 4.24 4.23 4.64 4.98 5.34 8.70 12.65

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4.3. Sediment transport rate The concept of making a sediment transport model based on the jump length goes back at least to Einstein (1950) (in Yalin, 1977) and recently developed by Nielsen (1992), in which the sediment transport rate is related to the weight or number of particle in motion (pick up function) and also their destination. The latter is considered in this paper thoroughly. With this view, the jump length data can be potentially applied to sediment transport rate of highly asymmetrical flows including in the swash zone. In this regard, the limited experiment on the number (weight) of particle in motion (Shanehsazzadeh and Holmes, 2010) revealed that at low flow regimes the number of particles in motion are less than total surface particles and when flow velocity increases, the number will increase up to the level more than the number of particles on surface. This clearly state that the sediment mode of transport gradually alters from bed load to sheet flow. More detailed results will be presented in the future when the data set is completed. 4.4. Application of the results for the swash zone The laboratory experiments of the present study are conducted to spot a light on the sediment motion in bed load transport under single highly asymmetric waves, which is intended to produce conditions that resemble swash motion. For the sake of simplifying and in order to reduce number of affecting external parameters, the flow regimes produced in this study are not fully identical with what is experienced in the swash zone. Hence, it is crucial to discuss the considerations for application of the results obtained in this study for the swash zone. The produced single waves in the laboratory gain the advantage of being highly asymmetric with near bed velocity and duration same as and close to the real flow condition in the swash zone, respectively (Fig. 1). Transfer of turbulence kinetic energy due to wave (bore) breaking to the boundary layer is also observed to some extend in the produced near bed velocity time series (Fig. 4); the level of realism however cannot be inspected at this stage. Nevertheless, there are some aspects of the swash process that are intentionally or due to limitations overlooked in the experiment. First and the most important is that in the experiments uprush is solely considered and the backwash is discarded. Obviously, Swash zone hydrodynamics governs sediment transport mechanisms during uprush and backwash flux of water. However, it is useful to consider two phases of the swash cycle, separately (Hughes et al., 1997). Then, the application of results obtained in up-rush flow condition for backwash, can be assessed through the level of influences of differential parameters of two phenomena (Section 4.2). Another phenomenon which is not considered in this study is infiltration/exfiltration, as the experiments are conducted in fully wet conditions. Two possible effects can be conceived from the phenomenon of in/exfiltration: (i) modification of effective weight of sediment particles (Horn et al., 1998; Turner and Masselink, 1998) and (ii) change in thickness of boundary layer (Conley and Inman, 1994; Nielsen, 2002). Holmes et al. (2002) argued that the degree of influence of the phenomena depends on the pressure gradient in the bed and in coarse grains of d >2 mm (with which the present study deals) no significant pressure gradient is anticipated, due to high porosity. Hoque and Asano (2007) developed a numerical model to calculate the wave-induced in/ exfiltration flows across the beach face under swash up-rush and backwash motions. Based on a parametric analysis they found that for coarse particles, boundary layer modification is dominant since the transport rate being onshore direction. Considering the influences of this phenomenon on the response of particles to a single swash event is therefore significant and must be considered in further experimental studies. The information provided by the present controlled laboratory tests is limited to only one size of sediment particles and within the

available range of asymmetric wave events. Clearly, generalization of the results requires further experimental and analytical efforts, using different sizes of sediment and a greater range of flow regimes. 5. Conclusion Hydrodynamics and sediment transport in the swash zone are unique and very complex phenomena. To achieve a robust model for predicting sediment motion in the swash zone and possible shoreline change one requires in-depth understanding about the behavior of sediment particles in highly asymmetric waves that continuingly uprush the beach face and retrieve in backwashes. This study presents a piece of valuable laboratory data to address the internationally accepted need for further evidences regarding how sediment grains are picked off the bed and transported in the swash zone (Puleo and Butt, 2006). However, the best approach to deal with such complex field of study might be considering the effects of each factor, separately. This allowed one to consider a physical system with a reduced number of involved parameters, but yet capture some of the realism of the situation. The experiments are conducted in this study to provide some information about the particle responses in terms of jump length against asymmetric waves similar
to the swash zone. The results in terms of average jump length JL show that despite reduction of many inherent involving parameters, jump length is still a stochastic parameter. The experiments showed that the probability distribution of jump length is quite wide (large variance) and skewed, different from that of saltation length in steady unidirectional flow, in which the distribution is close to normal and independent from the flow intensity. With considering the integral of excess energy of an arbitrary single wave over its duration, parameter sigma, as rational and meaningful representative of flow condition, a regression curve which fits most of the data of JL versus the flow parameter sigma shows that the rate of jump length declines from a linear increment. Moreover, the data corresponding to energetic, highly fluctuating flow regimes follow the same trend. The extrapolation of the regression line to more energetic flow conditions cannot be validated without more experiments conducted at greater values of sigma but with less flow fluctuations. The experiment on a slope of 10° revealed that, the average jump lengths also show the same trend as on the horizontal bed. It is obvious that the flow condition that simulated in this study is not identical to what is experienced in the swash zone; the influencing phenomena such as in/exfiltration (Holmes et al., 2002) and its effect on boundary layer and virtual particle weight, frequent wet and dry of the beach face and collision of uprush and backwashes (Holland and Puleo, 2001) are among those which are not considered in this study. Nevertheless, the present study shows that some parameters such as acceleration or generally the shape of the time-history could not be very important in comparison with other parameters such as content of energy, at least for bed load or sheet flow mode of transport of coarse particles. The information provided here is limited to only one size of sediment particles and within the available range of asymmetric wave events. Clearly, generalization of the results requires further experimental and analytical efforts, using different sizes of sediment and a greater range of flow regimes. However, the results illuminate some dark aspects of sediment transport in the flow regime that we experience in the swash zone and provide data for calibration/validation of the numerical simulation of particle motion at micro scale. Acknowledgment The funding of the experimental work is provided by the Ministry of Science, Research and Technology, Iran for PhD study of the first author in the Imperial College, London. The authors would like to appreciate

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