Very small waves and associated sediment resuspension on an estuarine intertidal flat

Estuarine, Coastal and Shelf Science 93 (2011) 449e459

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Very small waves and associated sediment resuspension on an estuarine intertidal flat Malcolm O. Green NIWA (National Institute of Water and Atmospheric Research), P.O. Box 11-115, Hamilton, New Zealand

a r t i c l e i n f o

a b s t r a c t

Article history: Received 27 January 2011 Accepted 21 May 2011 Available online 2 June 2011

Field data from a microtidal estuarine intertidal flat (Tamaki estuary, New Zealand) are used to analyse very small waves (height <10 cm; period 1.0e1.8 s) and associated sediment resuspension under light winds. Mean spectral period at the bed varied over the tidal cycle, driven by changes in surface-wave spectrum and depth-attenuation of orbital motions. Wave-orbital currents exceeded 30 cm/s, disturbing the fine-sand (100e200 mm) matrix of the seabed and resulting in the release of fine silt (particle size <20 mm) at concentrations >120 mg/L. Resuspension was initiated when w40% of the maximum zerodowncrossing orbital speeds in a burst exceeded the critical speed for initiation of sediment motion. Sediment concentrations were highest around low tide, when waves were smaller compared to high tide because of a reduced fetch but depth-attenuation of orbital motions was less because the water was shallower. Wave period exerted a control on sediment resuspension through the wave friction factor. There was a hysteresis in the wave Reynolds number such that it was greater on the ebbing tide compared to on the flooding tide: since it did not exceed 3
105 the bed was hydraulically smooth, and the wave friction factor therefore is inversely proportional to wave period. Hence, the tidal-cycle hysteresis in wave Reynolds number translated into a smaller wave friction factor on the ebbing tide, and accounting for this caused the ebb and flood sediment concentration data to collapse onto one curve when plotted against wave-induced skin friction. A simple model is presented to evaluate the relative contribution to sediment resuspension of waves associated with weak and strong winds. At the base of the flat (waves competent to resuspend sediment for 5% of the inundation time), waves associated with stronger, infrequent winds dominate resuspension. At the top of the flat (waves competent to resuspend sediment for 30% of the inundation time), waves associated with lighter, frequent winds dominate resuspension. Moderate winds e neither the strongest nor most frequently occurring e dominate resuspension integrated across the profile. The mass of sediment resuspended by waves is greatest towards the top of the flat: shoreward of this, resuspension is smaller because of wave dissipation; seaward of this, resuspension is smaller because of greater depth-attenuation of orbital motions. The location of maximum sediment mass resuspended by waves and the location of maximum duration of resuspension are not necessarily the same. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: intertidal flat waves sediment resuspension wave friction factor New Zealand

1. Introduction That wind waves play a central part in resuspending bed sediments and any attached contaminants from microtidal, estuarine intertidal flats is by now well established through field studies (e.g., Anderson, 1972; Ward et al., 1984; de Jonge and van Beusekom, 1995; Shoelhamer, 1995; Green et al., 1997; Green and MacDonald, 2001; Talke and Stacey, 2003, 2008; Green and Coco, 2007) and through modelling (e.g., Carniello et al., 2005). By initiating dispersal, wave resuspension contributes to the cleansing of

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heavy metal-contaminated sediments (Williamson et al., 1996). Particulate matter resuspended by waves affects bivalve condition (Ellis et al., 2002) and water-column light climate (Lawson et al., 2007; Verspecht and Pattiaratchi, 2010), with consequences for seagrass health and distribution (Turner et al., 1999; Moore and Wetzel, 2000; Zharova et al., 2001). The waves themselves, through pressure fluctuations and stresses induced by orbital motions, influence the recovery of benthic macrofauna from deposition events (Norkko et al., 2002) and drive biogeochemical processes (Vopel et al., 2005). Recognising the role that waves play, a number of model studies have linked spatial patterns of wavegenerated bed shear stress to the evolution of estuarine geomorphology, offering an explanation for the commonly-observed

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bimodal distribution of bathymetry (i.e., intertidal flats and saltmarshes) in microtidal estuaries (Fagherazzi et al., 2006, 2007). Marani et al. (2010) have extended this type of model to include with the waves the effects of intertidal vegetation and benthic microbial assemblages and demonstrated how tidal landforms may arise as alternative, but possibly coexisting, stable states. Wind waves typically occur episodically, and at any given site there will be a distribution of wave heights and periods, linked to the distribution of wind speeds and directions through the geometry and bathymetry of the estuary. Even though Anderson (1972) reported sediment resuspension by very small waves, field studies of sediment dynamics since have tended to focus on the more energetic waves in the distribution e the waves associated with wind storms e simply because “more happens” during those events. This has reinforced what now seems a fundamental dichotomy: the distinction between calm-weather forcing, which does not include waves, and storm forcing, which does include waves (e.g., Christie et al., 1999). However, even the casual observer of the sea will be aware that estuaries can become turbid, particularly around the edges, even in mild breezes, and that this turbidity is linked to the very small waves that lap the shore under those conditions. How significant are these more common conditions to the life and geomorphological evolution of estuaries? Modellers are faced with the question of specifying wind/wave conditions for their simulations. A rational response is to work with a “geomorphologically significant wind speed” (e.g., Fagherazzi and Wiberg, 2009), which balances magnitude and frequency of occurrence. Less commonly, Monte Carlo simulations based on a distribution of winds are employed. For instance, Fagherazzi et al. (2007) used a Monte Carlo simulation to show that the transition from intertidal flat to saltmarsh depends on statistical properties of the wind distribution (specifically, the timing and duration of calms and storms) but they did not discuss how the different components of the distribution contributed to that result. The aim of this paper is to assess the influence of very small but frequently occurring wind waves on the sediment dynamics of an estuarine intertidal flat. Field data are analysed with a view to describing waves and associated sediment resuspension under weak winds. These are the waves that occur during what would ordinarily be thought of as calm weather, and which therefore do not fit readily into the calmestorm dichotomy mentioned above. A simple model is presented to evaluate the relative contribution to intertidal flat sediment dynamics of waves associated with weak and strong winds. The results will demonstrate that very small waves should not be dismissed a priori from any consideration of sediment processes on intertidal flats. 2. Data Measurements of pressure, current velocity (two orthogonal components of the horizontal current and the vertical current) and infrared optical backscatter were obtained on an intertidal flat in the Tamaki Estuary, 15 km to the east of Auckland City central business district on the east coast of the North Island of New Zealand (Fig. 1). The Tamaki Estuary is w17-km long, roughly funnelshaped and occupies the valley of the ancestral Tamaki River, which was drowned during the Holocene sea-level rise (Abrahim, 2005). The field site was in an inner basin of the estuary, with wind fetches restricted by surrounding land and the Tohuna Torea sandspit that lies between the field site and the mouth of the estuary (Fig. 1). Measurements were made over two tidal cycles (lowehighelow) on 26 March 2003. Time series of pressure p(t) were acquired by a Druck ceramic pressure sensor mounted 25 cm above the bed. Sampling frequency was 5 Hz; there were 256 points per

burst (burst duration 51.2 s); and the burst interval was 4 min. Burst-averaged water depth h was computed from p(t) using the hydrostatic equation with a constant water density (1025 kg/m3) and measured atmospheric pressure. As a check, estimates of h were compared to measurements of water depth made with a metre stick on 10 occasions throughout the tidal cycle. Time series of current velocity were acquired by a Sontek ADV with the measurement volume located 10 cm above the bed. Sampling frequency was 16 Hz; there were 2048 samples per burst (128 s burst duration); and the burst interval was 4 min. The streamline components U, V, W of the current were calculated from the measured components U1, U2, U3 (where 1 and 2 denote nominal horizontal; 3 denotes nominal vertical) such that U ¼ W ¼ 0. The wave components of the total current UW, VW, WW (normal to wave crest, parallel to wave crest, vertical) were calculated from the streamline components such that the maximum variance was on UW; VW was orthogonal to UW; and WW ¼ W. The seabed at the site was virtually flat, with no sign of ripples or any other marks. The bed sediment was bimodal, with fine silt (particle size < 20 mm) embedded within a fine-sand matrix (100e200 mm). The percentage of fine silt in the matrix was w10%, and it did not confer any obvious cohesiveness to the bed. Infrared optical backscatter was measured at 10 cm above the bed with a Seapoint OBS, using the same sampling schedule as that used for pressure. Analysis of suspended-sediment samples was done using a Galai time-of-transition laser particle sizer. The analysis of samples from the time of greatest suspended-sediment concentration revealed that the median grainsize of the suspended sediment in terms of particle volume was 100e200 mm, but the actual number of particles that corresponded to was very few. In terms of numbers of particles, the median grainsize corresponded to 10e20 mm. Calibration tests using a laboratory tank demonstrated that the Seapoint OBS is at least 10 times more sensitive to the 10e20 mm particles than to the 100e200 mm particles. Hence, the Seapoint will have preferentially “seen” the smaller grainsizes at the Tamaki site, and for that reason a calibration curve developed for the 10e20 mm particles from the site was applied to convert optical backscatter intensity into burst-averaged suspended-finesilt concentration C. The site was exposed to air at low tide, and the depth was w1.25 m at high tide. The mean current reversed at high tide and reached a peak speed of w10 cm/s (at 10 cm above the bed) around mid-tide. The wind, which was light and steady at about 5 m/s, generated very short and small waves (Fig. 2), which are the subject of this analysis. Suspended-fine-silt concentration peaked around low tide at w120 mg/L and was zero around high tide. This temporal pattern is indicative of wave-induced sediment resuspension (e.g., Green et al., 1997, 2000).

3. Results Variation in the “intrinsic” properties of the waves e wave height and period e is approximately explainable in terms of the variation over the tidal cycle of the fetch. Fig. 3 shows the variation over the tidal cycle of root-mean-square wave height HRMS defined as:

HRMS

" Z ¼ 2 2

1:1 Hz 0:2 Hz

#1=2 ShðtÞ ðf Þd f

(1)

where the sea-surface elevation spectrum ShðtÞ ðf Þ was calculated from the measured current spectrum by using linear wave theory:

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Fig. 1. (a) Location e east coast of North Island of New Zealand. (b) Location e Tamaki Estuary. (c) Location e inner basin of Tamaki Estuary. (d) Model schematisation.

h i ShðtÞ ðf Þ ¼ SUW ðz;tÞ ðf Þ þ SVW ðz;tÞ ðf Þ

sinhkh h  i ucosh k z þ h

(2)

where SUW ðz;tÞ ðf Þ is the spectrum of Uw measured at elevation z above the bed, SVW ðz;tÞ ðf Þ is the spectrum of Vw measured at elevation z above the bed, f is frequency, u ¼ 2pf is radian frequency, k is linear-theory wavenumber corresponding to u and h, and the spectra are truncated at 1.1 Hz to avoid spurious amplification of high-frequency signals (including turbulence) in the current time series. HRMS increased from w4 cm at low tide to w10 cm at high tide, then reduced to w6 cm at the next low tide. The estimates of HRMS are approximately consistent with JONSWAP fetch-limited predictions, accounting for the change in fetch and

a veering of the wind from the north to the northeast (while remaining steady at 5 m/s) during the tidal cycle (Table 1). Here, HRMS predicted by JONSWAP is:

HRMS ¼ 0:707

1=2  2 UWIND gFx 0:0016 g UWIND

(3)

(Massel, 1996) where Fx is the fetch, g is acceleration due to gravity, UWIND is the wind speed along the fetch, and the units are m and s. The increase in fetch caused by the veering of the wind therefore accounts for the observed hysteresis in HRMS. Sea-surface elevation spectra ShðtÞ ðf Þ are shown in Fig. 4 grouped by phase of the tide as indicated by the inset figure, which shows the variation of h over the tidal cycle. The change in peak spectral

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T ¼ 2pm0 =m1

(5)

where mn is the nth moment of ½SUW ðz;tÞ ðf Þ þ SVW ðz;tÞ ðf Þ:

Z mn ¼

Fig. 2. Waves during the field deployment, around low tide. The significant wave height is w5 cm and the mean spectral period at the surface is w1 s. The white and black bands on the staff are 10 cm long; the cable runs to the current-meter probe.

period TP of ShðtÞ ðf Þ over the flooding tide (from w1.0 s at the beginning of the flood tide to w1.3 s by high tide) is also consistent with JONSWAP fetch-limited predictions (Table 1). Here, TP predicted by JONSWAP is:

TP ¼ 0:286

UWIND gFx 2 g UWIND

!1=3

10

8

HRMS (cm)

0

h i f n SUW ðz;tÞ ðf Þ þ SVW ðz;tÞ ðf Þ d f

6

Flood Ebb 4

0.75

1.25

h (m) Fig. 3. Variation of root-mean-square wave height with water depth over the tidal cycle.

(6)

T varied in a complicated fashion over the tidal cycle between about 1.0 and 1.8 s, which is likely to be related to the changes in ShðtÞ ðf Þ already elucidated and to changes over the tidal cycle in the depthattenuation of the orbital motions, which, in turn, depends on the water depth relative to the wave length. The following analysis is an attempt to tease out the way these two factors (changes in ShðtÞ ðf Þ; changes in depth-attenuation) controlled the observed variation in T over the tidal cycle. Wave period at the bed will turn out to an important control on sediment resuspension. Using linear wave theory and assuming a monochromatic wave train of radian frequency u, at any particular reference time tREF in the tidal cycle when the mean water depth is htREF and u corresponds to a wavenumber of ktREF , the measured wave-orbital motion UW ðz; tÞtREF at elevation z above the bed is related to the sea-surface elevation hðtÞtREF as:

h

UW ðz; tÞtREF ¼



hðtÞtREF ucosh ktREF z þ h  sinh ktREF h



i

tREF

(7)

tREF

(4)

(Massel, 1996). However, the continued increase in TP after high tide (reaching w1.7 s by the end of the ebb), cannot be explained by the JONSWAP model, since the fetch contracts on the ebbing tide, which cannot be reconciled with an increase in period using a steady-state model. The discrepancy between the observation and the JONSWAP prediction could be explained by an apparent stretching of the length of the waves arising from the wave field propagating against the steady flow of w5 cm/s on the ebbing tide, but calculations of wave stretching with a Doppler model revealed that that effect could only increase the apparent wave period by a tenth of a second or so. The variation over the tidal cycle in the mean spectral wave period T at the level of the pressure sensor (i.e., virtually at the seabed) is shown in Fig. 5, where T was computed following Longuet-Higgins (1975):

0.25

N

The wave-orbital motion at any other time in the tidal cycle ti will be related to the wave-orbital motion at tREF as:

h  i   cosh kti z þ h sinh ktREF h ti tREF  i  h  UW ðz; tÞti ¼ UW ðz; tÞtREF cosh ktREF z þ h sinh kti h tREF

jt ctREF ¼ UW ðz; tÞtREF i jtREF cti

ti

(8)

where the depth changes from htREF at time tREF to hti at time ti and hðtÞti ¼ hðtÞtREF . Because the wave field is assumed to be linear, this reasoning can be applied at every frequency in the wave-orbitalmotion spectrum to yield an expression for the spectrum at any time in the tidal cycle:

"

SUW ðz;tÞ ðf Þti ¼ SUW ðz;tÞ ðf ÞtREF

jti ctREF jtREF cti

#2

(9)

where ShðtÞ ðf Þti ¼ ShðtÞ ðf ÞtREF . Having obtained SUW ðz;tÞ ðf Þti , equation (5) may be applied to estimate the mean spectral period at elevation z above the bed. This method of calculating how the mean spectral period at the bed changes over the tidal cycle with changes in water depth was applied to the phases FLOODeA, FLOODeD and EBBeA shown in the inset in Fig. 4. The reference spectrum SUW ðz;tÞ ðf ÞtREF for phase FLOODeA was set to the spectrum measured at the start of the flood; for phase FLOODeD it was set to the spectrum measured at the start of that phase; and for phase EBBeA it was set to the spectrum measured at the end of that phase. The results of the analysis are shown by the three heavy lines in Fig. 5. In each of these phases of the tide, the heavy line tracks the measured T at the bed quite closely, confirming that attenuation alone can explain the variation in wave period at the bed; that is, no change in the surface spectrum is necessary to explain the change, and indeed none is obvious in Fig. 4. For the other phases (FLOODeB, FLOODeC, FLOODeE and EBBeB) a similar analysis was conducted, but the predicted changes in T did not match the measured changes. This indicates that the surface-wave spectrum in these phases of the tide was changing continuously (despite their appearance in Fig. 4). Shown in Fig. 6 are measured wave-by-wave (not burstaveraged) currents defined on the basis of a zero-downcrossing

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Table 1 Measured and predicted (JONSWAP fetch-limited) intrinsic properties of the waves. The JONSWAP predictions account for the veering of the wind from the north to the northeast (while remaining steady at 5 m/s) during the tidal cycle. Wind speed (m/s)

Low tide before flood High tide Low tide after ebb

5 5 5

Wind direction (degrees N)

Fetch (m)

N NNE NE

1200 2200 1700

analysis of UW(t), as shown in Fig. 7, where UW(t) is the current normal to the wave crest. U W is the burst-mean of UW(t), which is not necessarily zero. This will be referred to as the “steady” current. UZDCþ is the maximum zero-downcrossing current excursion from U W in the positive direction and UZDC is the maximum zerodowncrossing current excursion from U W in the negative direction (UZDC is expressed as a negative number). These will be referred to as the “wave-orbital” currents. Both U W þ UZDCþ and U W þ UZDC , with the steady current added, will be referred to as the “total” current. Also shown in Fig. 6 is the burst-averaged suspended-fine-silt concentration C measured at 10 cm above the bed. Wave-orbital currents were larger at low tide compared to at high tide, even though HRMS was larger at high tide. The reason is that depth-attenuation of wave-orbital motions was greater at high tide. Wave-orbital motions were larger at the end of the ebb (exceeding 30 cm/s) compared to at the beginning of the flood (20 cm/s). The reason is that depth-attenuation was less at the end of the ebb when the waves were longer period. Total currents were larger (nearly 40 cm/s at the end of the ebb and 30 cm/s at the start of the flood) than wave-orbital currents; nonetheless, C seemed to respond more to the wave-orbital currents, as evidenced by C approximately tracking UZDCþ and UZDC, but not U W þ UZDCþ and U W þ UZDC . The different relationships between C and the wave-orbital current on the one hand and between C and the total current on the other hand are brought out in Fig. 8 by plotting EZDC and ETOT against C (EZDC and ETOT are also plotted in Fig. 6). EZDC is the percentage of zero-downcrossing waves in each burst for which MAXðjUZDCþ j; jUZDC jÞ (i.e., the wave-orbital current) exceeds UW,CRIT, where UW,CRIT is the critical wave-orbital speed for initiation of sediment motion predicted by Komar and Miller (1973, 1975):

HRMS (cm)

TP (s)

Measured

JONSWAP

Measured

JONSWAP

6 9 7

4 10 6

1.1 1.4 1.2

1.0 1.3 1.7

2 rf UW;CRIT  1=2  ¼ 0:21 AW;CRIT =D rs  rf gD



(10)

In a comparison against a “wave-stress” theory, which required the specification of a wave friction factor, and a “wave-pluscurrent-stress” theory, which used a full wave-current boundarylayer model, Green (1999) showed that Komar and Miller’s “wave-orbital speed” theory (equation (10)) performed the best at predicting the onset of sand resuspension under irregular ocean waves. Green and MacDonald (2001) have since demonstrated that Komar and Miller’s theory is also a good predictor of the onset of resuspension of fine-sand sediments by waves on an estuarine intertidal flat. In equation (10), D is the bed-sediment grainsize, rs is sediment density (2.65 g/cm3) and rf is water density (1.025 g/cm3). AW,CRIT is the seabed orbital semi-excursion at initiation of sediment motion: UW; CRIT ¼ 2pAW; CRIT =T, where T is a wave period. For evaluating UW,CRIT, T was taken to be the zero-downcrossing period TZDC (see Fig. 7), and the sediment grainsize was taken to be 0.2 mm (which is the grainsize of the fine-sand matrix within which the silt component was embedded). Note that UW,CRIT was calculated individually for each zero-downcrossing wave for the purposes of determining EZDC. Likewise, ETOT is the percentage of zero-downcrossing waves in each burst for which MAXðjU W þUZDCþ j; jU W þ UZDC jÞ (i.e., the total current) exceeds UW,CRIT. Fig. 8 shows that the onset of sediment resuspension occurred when w40% of the maximum wave-orbital speeds in a burst exceeded UW,CRIT. In contrast, there is no obvious relationship between the total current and resuspension, including the case when ETOT reached 100% but C was zero. Fig. 6 suggests, and Fig. 9 more clearly reveals, a strong relationship between C and the burst-averaged zero-downcrossing wave-orbital acceleration defined as:

Fig. 4. Sea-surface elevation spectra, grouped by phase of the tide for clarity (inset). The tide rises anticlockwise from the bottom left corner.

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an effect of wave period on C, viz. the wave friction factor will account for the period effect, with the result that flood- and ebbtide C will collapse onto the one curve when plotted against a bed shear stress (as opposed to a current speed). Fig. 12, which plots C against the dimensionless wave-induced skin friction 0 U2 q0W ¼ 0:5fW r r r WAVE =f½ð s  f Þ= f gDg, tests that proposition. Here, 0 is the skin-friction wave friction factor and U fW WAVE, the characteristic wave-orbital speed at the bed, was estimated as the burst average of MAXðjUZDCþ j; jUZDC jÞ. Since the bed was hydraulically 0 was calculated from the wave Reynolds number using smooth, fW equation (12). Accounting for the period-dependence of the smooth-bed fW in this way does have the effect of approximately collapsing the ebb and flood data onto the one curve (compare Fig. 10 with Fig. 12). To reinforce the point, C is also shown in Fig. 12 0 plotted against qW calculated using a rough-turbulent wave friction factor:

Flood Ebb

1.6

T (s)

EBB-A FLOOD-D

1.2

= T of reference spectrum = T of spectrum predicted by equation (9)

FLOOD-A

0.8

0.25

0.75

h i 0 fW ¼ exp 5:213ðkB =AW Þ0:194 5:977

1.25

h (m) Fig. 5. Variation of mean spectral wave period at the bed with water depth over the tidal cycle. The curves show those periods when the change in T can be explained entirely by changes in depth-attenuation of wave-orbital motions. During the other periods, changes in the sea-surface elevation must also be invoked to explain changes in T.

(13)

(Nielsen, 1992) where kB is the hydraulic roughness of the seabed, evaluated as 2.5D/30, and AW was evaluated as the geometric burstaverage of MAXðjUZDCþ j; jUZDC jÞTZDC =2p. The ebb and flood data are further separated from each other when the rough-turbulent friction factor is used. 4. Discussion

lZDC ¼

n 1X

n i¼1

ðjUZDCþ j  jUZDC jÞi =TZDCi

(11)

where n is the number of zero-downcrossing waves in the burst. This implies that wave period exerts a strong control on sediment resuspension, which is reinforced by Fig. 10, which plots C against the square of the burst average of MAXðjUZDCþ j; jUZDC jÞ. (For simplicity, the latter term is called simply the “square of the waveorbital speed”.) Fig. 10 reveals that there is a different relationship between C and the square of the wave-orbital speed on the flooding tide compared to that on the ebbing tide, which might be due to a wave-period effect. Dimensional analysis shows that the wave friction factor fW can be expected to depend on the wave Reynolds number REW and the relative roughness of the wave boundary layer (Nielsen, 1992), where REW is given by A2W u=y, with AW ¼ UWAVE =u the characteristic seabed wave-orbital semi-excursion, u a characteristic wave radian frequency, y the molecular kinematic viscosity of water, and UWAVE a characteristic wave-orbital speed at the bed. For the fully developed rough-turbulent regime, the REW dependence disappears, leaving a dependence on the relative roughness only. For a hydraulically smooth bed, which holds for REW < z3
105 , laminar-flow theory is a reasonable approximation, and the wave friction factor therefore depends only on REW, as follows:

fW ¼ 2=

pffiffiffiffiffiffiffiffiffiffi REW

(12)

(Nielsen, 1992). Shown in Fig. 11 is the variation over the tidal cycle in REW, estimated as the geometric burst-average of ½MAXðjUZDCþ j; jUZDC jÞ2 TZDC =2py. Driven by changes in (primarily) wave period and (secondarily) wave height over the tidal cycle, there was a strong hysteresis in REW such that it was significantly greater on the ebbing tide compared to on the flooding tide. REW also fell well within the smooth-bed regime 1=2 (equation ðREW < z3
105 Þ, in which case fW varies with REW (12)). This results in the wave friction factor being larger on the flooding tide compared to on the ebbing tide (Fig. 11). The marked difference in wave friction factor on the ebbing tide compared to on the flooding tide provides a plausible mechanism for accounting for

Very small, short-period waves associated with light winds can resuspend bed sediments on this estuarine intertidal flat. 0 The data in Fig. 12 indicate a value for qW of w0.06 at the onset of resuspension, which is approximately the critical Shields parameter for initiation of granular sediment transport on a flat, unconsolidated bed of sediment grainsize 0.2 mm (Graf, 1971; van Rijn, 1993). This suggests that suspended sediment at the Tamaki site resulted from the release of the fine silt (<20 mm) from the seabed fine-sand (100e200 mm) matrix by wave-generated fluid forces acting on the particles in the fine-sand matrix. We now address the question of which is more effective over the long term e small waves associated with frequent light winds or larger waves associated with infrequent stronger winds e using the Tamaki site as the test case. For this purpose, a simple model of waves over the Tamaki intertidal flat was constructed, as follows. Fig. 1(d) shows the model bathymetry, which is intended as a simple schematisation of a cross-section of the Tamaki basin along the north-northeast/south-southwest direction. This direction approximately presents the greatest fetch to the wind (Fig. 1), and is halfway between the direction of the wind during the flooding tide of the field experiment and the direction of the wind during the subsequent ebbing tide (Table 1). There is a 100-m wide channel in the middle of the domain, of arbitrary depth. Extending a horizontal distance of 1000 m to the north of the northern edge of the channel is a plane intertidal flat, which slopes upwards at 1.5:1000 from an elevation z0 ¼ 0 m at the base of the flat (where it meets the top of the channel edge) to z0 ¼ 1:5 m at the top of the flat. A southern intertidal flat mirrors the northern intertidal flat. There are 10 stations placed at 100-m horizontal distances along the southern intertidal flat, from z0 ¼ 0 m (station 1) to z0 ¼ 1:35 m (station 10). The field measurement site is located on the model southern intertidal flat, w200 m from the channel edge, which is close to model station 3. The model timestep was 30 min. The water level at each timestep was evaluated by applying a sinusoidal tide with period 12.5 h and amplitude 1.5 m. At low tide, the water level was at z0 ¼ 0 m; hence, the water was constrained to the channel and the intertidal

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Fig. 6. Measured wave-by-wave wave-orbital currents, total currents and wave-orbital acceleration; burst-averaged suspended-fine-silt concentration; and percentage of the zerodowncrossing waves in each burst for which the wave-orbital and the total currents exceed critical wave-orbital speed for initiation of sediment motion for 0.2 mm sand.

flats were dry. At high tide, the water’s edge was 100 m beyond station 10. The water depth h at each station was evaluated by subtracting the station elevation from the water level. At high tide, the water depth at station 10 was 0.15 m and at station 3 (where the TZDC

Uw(t), cm/s

25

UZDC+

20 15 10

Uw UZDC-

5 0 Uw+ UZDC-

Uw+ UZDC+

Fig. 7. Definitions of wave-by-wave currents. UW(t) is the measured current normal to the wave crest. U W is the “steady” current; UZDCþ and UZDC are “wave-orbital” currents (UZDC is expressed as a negative number); U W þ UZDCþ and U W þ UZDC are “total” currents.

field measurements were made) it was 1.20 m (compare with measured water depths in Fig. 4 inset). At each timestep a wind speed and fetch were specified, as follows. Wind speed UWIND and wind direction fWIND were taken sequentially from a 23-year half-hourly wind record (1987e2010) from Whangaparaoa weather station (agent number 1400, National Climate Database, http://cliflo-niwa.niwa.co.nz/pls/niwp/wgenf. genform1_proc) located 15 km north of the study site, on the open coast, north of Auckland city. If UWIND > 0 and fWIND fell between northwest and northeast (i.e., the wind was blowing from approximately the northern sector), then Fx at each station was evaluated from the model geometry given the water level at that time. No attempt was made to align the tidally-varying water level in the model with the wind observations since the relative phasing of the two over a long period of time is essentially random. If UWIND ¼ 0 or fWIND was outside the northern sector then that datapoint was discarded, and the wind record was interrogated until the next datapoint that satisfied the selection criteria was found. This procedure was intended to capture just the “wave-

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M.O. Green / Estuarine, Coastal and Shelf Science 93 (2011) 449e459

150

150 Flood Ebb

100

100

C (mg/L)

C (mg/L)

E ZDC E TOT

50

50

0

0 0

20

40

60

80

100

0

%

200

Square of wave-orbital speed (cm/s) 2

Fig. 8. Burst-averaged suspended-fine-silt concentration plotted against percentage of the zero-downcrossing waves in each burst for which the wave-orbital currents and the total currents exceeded the critical wave-orbital speed for initiation of sediment motion for 0.2 mm sand.

generating winds” in the analysis, which amounted to approximately 23% of the winds in the 23-year record. Having found a wave-generating wind, Fx and UWIND were applied in the JONSWAP fetch-limited equations to estimate HRMS (equation (3)) and TP (equation (4)) at each model station. Assuming Rayleigh-distributed waves, the significant wave height HSIG was estimated as 1.414HRMS (Longuet-Higgins, 1952). To account for steepness-limited wave breaking, HSIG was limited to 2p=½7ktanhðkhÞ (where k was the linear-theory wavenumber corresponding to TP and h), following Tayfun’s (1981) analysis of the local limiting form of an irregular wave packet. To account for depth-limited wave breaking, HSIG was limited to gh, where g was determined by calibration against the Tamaki data, as follows. The model was run for the day of the field observations, using a constant wind speed (5 m/s) and direction (northerly) as model input. Results with a value of 0.6 for g are shown in Fig. 13, plotted as measured water depth versus measured wave-orbital speed at the bed as represented by MAXðjUZDCþ j; jUZDC jÞ, and modelled water depth versus UWAVE extracted from model station 3. The modelled data with g ¼ 0.6 fall between the ebb-tide and flood-tide measurements. Recall that the hysteresis in the observations arose from a change in fetch caused by a slight veering of the wind: with its simple schematisation of the fetch, the model is incapable of reproducing the measurement hysteresis. (Tests with a more complicated model schematisation that more accurately

150 Flood Ebb

C (mg/L)

100

Fig. 10. Burst-averaged suspended-fine-silt concentration plotted against square of the wave-orbital speed (refer to text for precise definition).

reproduced fetches yielded no fundamental changes in the results that follow.) Nonetheless, the model does a good job of reproducing the data, and 0.6 was used as the calibrated value of g, which lies approximately midway in the range of values (w0.4e1.2) derived from theory and reported from field measurements in a range of open-coast surfzones (refer to Raubenheimer et al., 1996, for a brief review). The effect of wave dissipation by bottom friction is implicit in the depth-limitation of wave height: as Thornton and Guza (1982) point out, this simplification allows the wave energy (in the saturated surfzone) to be described everywhere without having to worry about the exact nature of the wave dissipation. Given TP and HSIG, these were then used to estimate the waveorbital speed at the bed UWAVE:

UWAVE ¼ pHSIG =sinhðkhÞ

where k is the linear-theory wavenumber corresponding to TP and h. In this way, a series of UWAVE corresponding to wave-generating winds was generated at each model station. Since w23% of the winds in the 23-year record were classified as wave-generating, the number of datapoints N in the UWAVE series was (approximately) 0.23
23 years
365 days/year
24 h/day
2 wind observations/ hour ¼ 92,680 points, or about 3700 tidal cycles. Shown in Fig. 14(a) is the distribution of wave-generating wind speeds. The most frequent (nearly 30%) is 3e4.5 m/s. Since wavegenerating winds occurred for w23% of the 23-year period of the wind record, 3e4.5 m/s wave-generating winds occur for w7% of the time. Fig. 14(b) shows the distribution by wind speed of I at each station, defined as:

Ij ¼

100

(14)

N X

6 Xi;j

(15)

i¼1

50

0 0

5

10

15

20

λZDC (cm/s2) Fig. 9. Burst-averaged suspended-fine-silt concentration plotted against burstaveraged wave-orbital acceleration.

where i is the datapoint number; j is the station number; X ¼ UWAVE if UWAVE > UW,CRIT and X ¼ 0 if UWAVE < UW,CRIT; and UW,CRIT was predicted by Komar and Miller (1973, 1975) with TP and D ¼ 0.2 mm. I is intended as an indicator of the mass of fine silt resuspended from the bed at each station by wave-orbital motions in the 23-year period 1987e2010. The logic behind the choice of 6 for the value of the exponent in (15) is that the Tamaki data show 03 0 that C is approximately proportional to qW (Fig. 12) and qW in turn varies with the square of the wave-orbital speed at the bed. The units for I are not shown since they are irrelevant: the purpose of this analysis is to determine the relative contributions of the different wind speeds (and therefore wave heights) to sediment

M.O. Green / Estuarine, Coastal and Shelf Science 93 (2011) 449e459 1.25

1.25 Flood Ebb

1.00

0.75

0.75

0.50

0.50

0.25

h (m)

h (m)

1.00

0.25 0

1000

2000

0.10

fw

REw

Fig. 11. Variation in wave Reynolds number and wave friction factor over the tidal cycle.

resuspension at different locations across the intertidal flat. Fig. 14(c) shows the distribution by wind speed of IPROFILE, which is the sum of I across the model profile:

IPROFILE ¼

10 X

Ij

(16)

j¼1

IPROFILE is intended as an indicator of the mass of fine silt resuspended across the entire profile (i.e., from stations 1 to 10 on the southern intertidal flat) by wave-orbital motions in the 23-year period 1987e2010. As above, units are not given for IPROFILE, for the same reason. Fig. 15 shows, for each station, the average percentage of the inundation time for which waves were “competent” to resuspend sediment, which is defined as UWAVE > UW,CRIT. The following discussion refers to Figs. 14(aec) and 15. At model station 3, where the field measurements were made, there is a broad peak in I extending from light winds (4.5e6 m/s) to stronger winds (13.5e15 m/s). The wind speed on the day of the Tamaki observations falls within the former wind-speed band, indicating that the very small observed waves (Fig. 2 shows photographs) do in fact make a significant contribution to fine-silt resuspension at the field site over the long term. At the base of the flat (deepest water, shortest fetches, longest inundation time), relatively strong (13.5e15 m/s) and infrequent (<1% of the wave-generating winds; <0.23% of the time) winds dominate resuspension. The reason is as follows. As the fetch increases with the rising tide at this outer station, the wave period does not increase fast enough to compensate for the attenuationwith-depth of the wave-orbital motions, with the result that

457

wave activity at the bed switches off quite early in the flooding tide (and switches on again quite late in the ebbing tide). When waves can reach down to the bed, the fetch is therefore quite small, and practically equivalent to the channel width. This makes the fetch effectively constant and, this being the case, stronger winds/larger waves therefore dominate wave resuspension. Waves here are competent to resuspend sediment for only a small fraction (w5%) of the inundation time. At the top of the flat (shallowest water, longest fetches, shortest inundation time), relatively light (4.5e6 m/s) and frequent (w22% of the wave-generating winds; w5% of the time) winds dominate resuspension. The reason is as follows. By the time the tide reaches stations at the top of the intertidal flat, maximum fetches have developed and wave periods (lengths) are long enough relative to the water depth to ensure that wave-orbital motions are capable of penetrating down to the bed for more of the tidal cycle (compared to at the base of the flat). However, as the water depth becomes shallower, more of the larger waves also become depth-limited by dissipation, thus reducing the difference between what start out as small and large waves. This has the result that resuspension tends to become dominated by the more frequently occurring waves, which are the smaller waves. When there is wave-driven sediment resuspension at the top of the flat, it is therefore dominated by smaller waves. Waves here are competent for w30% of the inundation time. Moderate winds (7.5e9 m/s; w7.5% of the wave-generating winds; w1.8% of the time) dominate resuspension integrated across the profile, IPROFILE. These winds are neither the strongest nor the most frequently occurring. I, the mass of sediment resuspended by waves, is greatest towards the top of the intertidal flat, at station 9. Here, moderate winds (7.5e9 m/s; w7.5% of the wave-generating winds; w1.8% of the time) dominate resuspension. Shoreward of station 9 I is smaller because of wave dissipation; seaward of station 9 I is smaller because wave-orbital motions experience greater depthattenuation. However, waves are competent for nearly 50% of the inundation time at both stations 7 and 8 (compare with w30% of the inundation time at station 9). Hence, the location on the flat of maximum sediment mass resuspended by waves and the location on the flat of maximum duration (as a fraction of the inundation time) of sediment resuspension by waves are not necessarily the same.

25 Wave-orbital speed at the bed

Flood Ebb

100

Measured - outer site - flood

20

C (mg/L)

Measured - outer site - ebb

cm/s

Modelled - flood

15

Modelled - ebb

10

C proportional to θw3

5

10 0

θw= 0.06

0.10

θw Fig. 12. Burst-averaged suspended-fine-silt concentration plotted against dimensionless wave-induced skin friction estimated using a smooth-bed wave friction factor (black symbols) and a rough-turbulent friction factor (grey symbols).

0.00

0.25

0.50

0.75

1.00

1.25

h (m) Fig. 13. Measured wave-orbital speed at the bed as represented by ðjUZDCþ MAXj; jUZDC jÞ at the field site, and modelled wave-orbital speed as represented by UWAVE (equation (14)) extracted from model station 3, where model predictions were made with a value of 0.6 for g.

Frequency

M.O. Green / Estuarine, Coastal and Shelf Science 93 (2011) 449e459 (% of all the wave-generating winds )

458

30

5. Conclusions

a

20 10 0 Station 9

b [linear scale]

Station 3, field measurements

Station 1, base of intertidal flat

28.5-30

27-28.5

25.5-27

24-25.5

22.5-24

21-22.5

19.5-21

18-19.5

15-16.5

13.5-15

12-13.5

10.5-12

7.5-9

9-10.5

6-7.5

4.5-6

3-4.5

1.5-3

0-1.5

[linear scale]

IPROFILE

c

16.5-18

I

Station 10, top of intertidal flat

Wind-speed range (m/s)

Fig. 14. (a) Distribution of wave-generating wind speeds, shown as a percentage of all the wave-generating winds. (b) Distribution by wind speed of I at each station, which is intended as an indicator of the mass of fine silt resuspended from the bed at each station by wave-orbital motions in the 23-year period 1987e2010. (c) Distribution by wind speed of IPROFILE, which is intended as an indicator of the mass of fine silt resuspended across the entire model profile (i.e., from stations 1 to 10 on the southern intertidal flat) by wave-orbital motions in the 23-year period 1987e2010.

% of inundation time waves are "competent"

Although the greatest contribution to IPROFILE may not always be towards the top of the intertidal flat (other intertidal flat geometries and wind climates could deliver different results), it does seem likely that the greatest contribution will never be from the base of the flat (because of fetch limitations), and neither will it be from the top of the flat (because of wave dissipation). This conclusion is consistent with recent modelling that shows a characteristic midflat maximum in wave-induced bed shear stress and associated erosion potential (e.g., Fagherazzi et al., 2006).

50 40 30 20 10 0 1

2

3

4

5

6

7

8

9

10

Model station number Fig. 15. Average percentage of the inundation time for which waves are “competent” to resuspend sediment, defined as UWAVE > UW,CRIT.

Very small (root-mean square wave height < 10 cm; mean spectral period at the bed 1.0e1.8 s) wind waves generated waveorbital currents at the bed that exceeded 30 cm/s. Wave-orbital currents were capable of disturbing the fine-sand (100e200 mm) matrix of the seabed, which released fine silt (particle size < 20 mm) into the water column at concentrations in excess of 120 mg/L at 10 cm above the bed. Suspended-sediment concentrations were highest around low tide, when waves were smaller compared to high tide because of a reduced fetch but depthattenuation of wave-orbital motions was less because the water was shallower. Resuspension was initiated when w40% of the maximum wave-orbital speeds in a burst exceeded the critical speed for initiation of sediment motion predicted by Komar and Miller (1973, 1975). In contrast, there was no obvious relationship between total (wave plus steady) current speed and sediment resuspension. Wave period exerted a control on sediment resuspension through the wave friction factor. Driven by changes in (primarily) wave period at the bed and (secondarily) wave height over the tidal cycle, there was a strong hysteresis in the wave Reynolds number such that it was significantly greater on the ebbing tide compared to on the flooding tide. The wave Reynolds number did not exceed 3
105, which indicates that the bed was hydraulically smooth, and in this case the wave friction factor is inversely proportional to the wave period. Hence, the tidal-cycle hysteresis in the wave Reynolds number translated into a smaller wave friction factor on the ebbing tide compared to on the flooding tide. Accounting for the hysteresis in wave friction factor had the effect of approximately collapsing the ebb and flood concentration data onto the one curve when plotted against the wave-induced skin friction. Furthermore, the time-averaged suspended-silt concentration was found to be approximately proportional to the cube of the wave-induced skin friction. The distribution of wave-driven resuspension by wind speed (and therefore wave height), the fraction of the inundation time that waves are capable of resuspension, and the distribution of the mass of sediment resuspended by waves across an intertidal flat appear to be governed by the characteristics of the windspeed distribution together with subtle balances between the water depth and fetch, which vary over the tidal cycle and which play out in different ways on different parts of the intertidal flat. At the base of the intertidal flat, where waves were competent to resuspend sediment for only a small fraction (5%) of the inundation time, waves associated with stronger, infrequent winds dominate resuspension. At the top of the intertidal flat, where waves are competent to resuspend sediment for about 30% of the inundation time, waves associated with lighter, frequent winds dominate resuspension. Moderate winds e neither the strongest nor the most frequently occurring e dominate the resuspension integrated across the profile. The location on the flat of maximum sediment mass resuspended by waves and the location of maximum duration (as a fraction of the inundation time) of resuspension by waves are not necessarily the same. However, both lie above the base of the flat (where fetch limits wave activity at the bed) and below the top of the flat (where wave dissipation limits wave activity at the bed), which is consistent with model predictions of a characteristic midflat maximum in wave-induced bed shear stress and associated erosion potential. Very small waves, which occur more frequently than large waves, can play a significant role in resuspension of bed sediments on estuarine intertidal flats.

M.O. Green / Estuarine, Coastal and Shelf Science 93 (2011) 449e459

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