Suspended sediment transport in the swash zone of a dissipative beach

Transcription

1 Marine Geology 216 (25) Suspended sediment transport in the swash zone of a dissipative beach Gerhard Masselink a, T, Darren Evans b, Michael G. Hughes c, Paul Russell d a School of Geography, University of Plymouth, Plymouth, PL4 8AA, England, UK b Geography Department, Loughborough University, Loughborough, LE11 3TU, England, UK c School of Geosciences, University of Sydney, NSW 26, Australia d School of Earth, Ocean and Environmental Sciences, University of Plymouth, Plymouth, PL4 8AA, England, UK Received 23 April 24; received in revised form 18 January 25; accepted 17 February 25 Abstract Simultaneous high frequency field measurements of water depth, flow velocity and suspended sediment concentration were made at three fixed locations across the high tide swash and inner surf zones of a dissipative beach. The dominant period of the swash motion was 3 5 s and the results are representative of infragravity swash motion. Suspended sediment concentrations, loads and transport rates in the swash zone were almost one order of magnitude greater than in the inner surf zone. The vertical velocity gradient near the bed and the resulting bed shear stress at the start of the uprush was significantly larger than that at the end of the backwash, despite similar flow velocities. This suggests that the bed friction during the uprush was approximately twice that during the backwash. The suspended sediment profile in the swash zone can be described reasonably well by an exponential shape with a mixing length scale of.2.3 m. The suspended sediment transport flux measured in the swash zone was related to the bed shear stress through the Shields parameter. If the bed shear stress is derived from the vertical velocity gradient, the proportionality coefficient between shear stress and sediment transport rate is similar for the uprush and the backwash. If the bed shear stress is estimated using the free-stream flow velocity and a constant friction factor, the proportionality factor for the uprush is approximately twice that of the backwash. It is suggested that the uprush is a more efficient transporter of sediment than the backwash, because the larger friction factor during the uprush causes larger bed shear stresses for a given free-stream velocity. This increased transport competency of the uprush is necessary for maintaining the beach, otherwise the comparable strength and greater duration of the backwash would progressively remove sediment from the beach. D 25 Elsevier B.V. All rights reserved. Keywords: swash zone; sediment suspension; sediment transport; bed shear stress; dissipative beach T Corresponding author. address: gmasselink@plymouth.ac.uk (G. Masselink) /$ - see front matter D 25 Elsevier B.V. All rights reserved. doi:1.116/j.margeo

2 17 G. Masselink et al. / Marine Geology 216 (25) Introduction The swash zone is arguably the most dynamic part of the nearshore region and is characterised by large flow velocities, high turbulence levels and large suspended sediment concentrations (Elfrink and Baldock, 22). Swash provides the principal mechanism for sediment exchange between the subaerial and subaqueous zones of the beach (Masselink and Hughes, 1998; Puleo et al., 2) and a detailed understanding of this process is of vital importance to the modelling of shoreline evolution. Swash processes are directly forced by surf zone waves and are controlled by factors such as the beach morphology, sediment characteristics and beach groundwater (Hughes and Turner, 1999). Despite clear process and sediment linkages between the swash and surf zones, there are a number of features that uniquely characterise the swash zone: (1) very energetic flows prevail with velocities frequently exceeding 2 m s 1 (Hughes et al., 1997a; Masselink and Hughes, 1998; Butt and Russell, 1999; Osborne and Rooker, 1999; Puleo et al., 2, 23); (2) bore-related free-surface turbulence may impact on the bed during the uprush, contributing significantly to sediment suspension and transport (Puleo et al., 2; Jackson et al., 24); (3) both flow and sediment transport processes may be significantly affected by the vertical movement of water into and out of the beach (Turner and Masselink, 1998; Butt et al., 21; Masselink and Li, 21; Conley and Griffin, 24); (4) combined shallow water depths and large flow velocities during the backwash may result in super-critical flow conditions and hydraulic jumps (Osborne and Rooker, 1999; Butt and Russell, 1999); (5) suspended sediment concentrations are generally up to one order of magnitude larger than in the surf zone, attaining values in excess of 1 kg m 3 near the bed (Beach and Sternberg, 1991; Osborne and Rooker, 1999; Butt and Russell, 1999; Puleo et al., 2; Evans et al., 23); and (6) the combination of strong flows and large suspended sediment concentrations induces large sediment transport rates (Masselink and Hughes, 1998; Puleo et al., 2; Evans et al., 23), although the net transport rates may be a small difference between two large quantities (Osborne and Rooker, 1999). There have been several field measurements of swash zone sediment transport and all emphasise the difference between the uprush and backwash phases of the swash flow the backwash is not simply the reverse of the uprush (Hughes et al., 1997a). Most investigations have been carried out on steep beaches subjected to low waves (Horn and Mason, 1994; Hughes et al., 1997a; Masselink and Hughes, 1998; Puleo et al., 2, 23; Masselink and Li, 21; Jackson et al., 24). Under these conditions, swash motion is at wind-wave or swell frequencies with typical wave uprush and backwash durations of 3 5 s. These previous studies have related either the total or suspended load sediment transport rate q to the swash flow velocity u using simple transport models of the form q ~ u n. A key finding of these studies is that, for a given flow velocity, the uprush moves more sediment than the backwash. Masselink and Hughes (1998) attribute the greater sediment transport competency of the uprush to a number of factors not accounted for in the simple q ~ u n model, including flow acceleration (Nielsen, 22; Puleo et al., 23), swash-beach groundwater interactions (Turner and Masselink, 1998; Butt and Russell, 2) and the excess suspended sediment present during the uprush due to bore collapse (Hughes et al., 1997b; Jackson et al., 24). The role of borerelated turbulence is further addressed by Puleo et al. (2) who found a significant relationship between the amount of energy dissipated in a bore and the total immersed weight transport related to the bore. Several sediment transport studies have been conducted on gently sloping beaches subjected to high waves. Under these conditions the wind and swell waves are fully dissipated in the surf zone and the swash motion is at infragravity frequencies, with wave uprush and backwash durations exceeding 1 s (Beach and Sternberg, 1991; Osborne and Rooker, 1999; Butt and Russell, 1999). These studies all report the presence of large suspended sediment concentrations in the swash zone, but no efforts have been made to quantitatively relate sediment transport rates to flow conditions. Recent studies have elucidated some important aspects of swash flow dynamics, particularly the development of the swash boundary layer and the

3 G. Masselink et al. / Marine Geology 216 (25) role of bore turbulence. Cox et al. (1998) observed in the laboratory that the bed shear stress (derived from the logarithmic velocity profile in the boundary layer) during the uprush was generally greater than during the backwash. Similarly the inferred friction coefficient during the uprush was larger than during the backwash. Conley and Griffin (24) made direct field measurements of bed shear stress in the swash zone using flush mounted hot film anemometry and reported consistent results, with the maximum bed shear stress and the friction coefficient during the uprush being approximately double that during the backwash. These differences between uprush and backwash may be due to turbulence. The turbulent kinetic energy during the uprush is larger than during the backwash (Petti and Longo, 21; Cowen et al., 23), and this has been attributed to the advection of bore-related turbulence into the swash zone (Longo et al., 22). The presence of this excess turbulence in the water column is expected to delay the vertical growth of the boundary layer, increase bed shear stress and artificially raise the friction coefficient (Petti and Longo, 21; Puleo and Holland, 21). An alternative explanation for the larger bed shear stresses and friction coefficients during the uprush is the thinning of the boundary layer due to infiltration (Conley and Inman, 1994). Although this may provide an explanation for the field observations of Conley and Griffin (24), it does not apply to the laboratory measurements of Cox et al. (1998), which were conducted on an impermeable beach. This paper reports field measurements of hydrodynamics, sediment suspension and suspended sediment transport rates collected from a gently sloping swash zone subjected to energetic wave conditions. The swash motion in the present study is predominantly at infragravity frequencies and it is hypothesised that the sediment transport under such conditions is mainly driven by instantaneous bed shear stresses with bore turbulence playing a relatively minor role. 2. Methodology A 2-week field experiment was conducted in October November 21 on Perranporth Beach, Cornwall, England (Fig. 1). This beach is composed of medium sand (D 5 = mm) and is characterised by a low-gradient (tan b =.15.25), concave nearshore profile (Fig. 2). The beach experiences a mean spring tide range of 5.3 m and has an average significant wave height of approximately 1.4 m (Davidson et al., 1998). The beach faces west northwest and is exposed to swell from the Atlantic, but also receives locally generated wind waves. During the field campaign, morphological, sedimentological and hydrodynamic data were collected during 29 tidal cycles displaying a range of wave/tide conditions, but in the present paper only data collected around high tide on 27 October 21 will be discussed. Instruments were deployed at three fixed locations in the high-tide swash and inner surf zones (Fig. 2). At each location, the water velocity was measured using two mini (.32 m diameter discus head) Valeport electromagnetic current meters (ECM) deployed to record flow velocities at.3 and.6 m from the bed (Fig. 3). These were pre-calibrated by the manufacturer and offset drifts were found to be negligible. The water depth was measured using three miniature pressure transducers (PT) installed flush with the sand surface and at.2 and.4 m below the surface. These were calibrated using a Druck portable calibration unit, allowing the electrical output to be converted to an equivalent pressure. Atmospheric pressure, recorded when the PTs were emerged, was subtracted from the calibrated data and the water depth was determined by assuming that a pressure of.1 Pa is equivalent to a 1 cm head of water. A vertical array of miniature optical backscatter sensors (OBS) were used to measure the suspended sediment concentration at.1,.2,.3,.4,.5,.7,.1,.15 and.2 m from the bed. These were calibrated by suspending known quantities of local sediment in glycerol using the method developed by Butt et al. (22a). All instruments were synchronously logged at 8 Hz using shore-based computers. During the high tide discussed in this paper, the net vertical morphological change in the swash and inner surf zone was less than.1 m. Observations conducted during other tides using fluorescent sand tracer plugs indicate that instantaneous changes in the bed level are also less than.1 m (Evans, 24). It is therefore assumed that the instruments remained at their initial elevations throughout the high-tide measurement period.

4 172 G. Masselink et al. / Marine Geology 216 (25) Fig. 1. Location of Perranporth Beach, Cornwall, England. All instrument rigs collected continuous time series, but due to the episodic submergence of the instruments in the swash zone, a considerable amount of pre-processing was required prior to data analysis. The PT deployed flush with the bed was used to determine the swash depth. To avoid inclusion of very Elevation relative to CD (m) Uprush limit Backwash limit 6 Rig 1 Rig 2 Rig Cross-shore distance (m) Fig. 2. Beach profile showing position of instrument stations at high tide. The elevation is in meters above Chart Datum. shallow water depth data, resulting in drawn-out backwashes, the backwash was terminated when the water depth became less than.15 m. The output from the ECMs and OBSs was also controlled using the water depth measured with the top PT. Flow velocity and suspended sediment data were only considered for analysis when the instruments were covered by at least.5 m of water. Ideally, the total suspended sediment flux should be computed as the product of the vertical suspension profile and the vertical velocity profile. In the present study, the suspended sediment profile was derived from a total of nine OBSs, but flow velocity data are only available from two elevations in the water column (only one if the water depth is less than.65 m). The sediment flux was therefore computed by multiplying the suspended sediment profile by the current velocity measured at.3 m from the bed. Depending on the structure of the swash boundary layer, this approach results either in an underestimation (if the boundary layer is much thicker than.3 m) or an over-

5 G. Masselink et al. / Marine Geology 216 (25) Fig. 3. Photo showing the configuration of the sensors on the instrument rigs (PTs=pressure transducers; OBSs=optical backscatter sensors; ECMs=electromagnetic current meters; and ADV=acoustic Doppler Velocimeter). The ADV was not used in the present study. estimation (if the boundary layer is thinner than.3 m) of the actual suspended sediment flux. 3. Preliminary analysis Data were collected over a 3.5-h period around the night high tide of 27 October 21. Offshore wave conditions were characterised by a visually estimated significant wave height and period of 1.5 m and 12 s, respectively. Combined with the gentle beach gradient (tan b =.2), this resulted in extremely dissipative conditions characterised by a wide ( N 1 m) surf zone with numerous spilling breakers and a value for the surf scaling parameter (Guza and Inman, 1975) in excess of 1. The dissipative nature of the surf zone is clearly demonstrated by spectra computed from data collected in the inner surf zone (Fig. 4). Both the pressure and cross-shore current spectra are dominated by infragravity energy ( f b.4 Hz) and the water motion at the low-frequency end of the spectrum ( f b.1 Hz) is standing. Inspection of the raw time series further shows that shoreward-propagating bores with a period of about 3 s are Normalised spectrum p u.2.4 Frequency (Hz) Coherence Frequency (Hz) Phase Frequency (Hz) Fig. 4. Cross-spectral analysis of 1 h of pressure and cross-shore current data collected by Rig 3 around high tide: normalised spectra of pressure and cross-shore current velocity (left panel), coherence spectrum (middle panel) and phase spectrum (right panel). The frequency resolution of the spectra is.1 Hz and the degrees of freedom are 32. The small vertical bar in the corner of the left panel represents the 95% confidence interval. The dashed line in the middle panel represents the 95% significance level of the coherence computed according to Thompson (1979).

6 174 G. Masselink et al. / Marine Geology 216 (25) superimposed on this standing (far) infragravity wave motion. The nature of the water motion on an energetic, dissipative beach makes it difficult to identify the swash zone region. The swash zone is typically defined as that part of the beach that is submerged less than 1% of the time, whereas the surf zone is always submerged. On a dissipative beach, however, the nearshore water level is modulated by infragravity wave motion, causing the dswash zonet to occasionally experience surf zone bores, and the dsurf zonet to become intermittently exposed and subjected to swash action. Under energetic, dissipative conditions the boundary between swash and surf is therefore marked by a relatively wide transition zone. For the present purpose, the transition zone is defined as being characterized by an inundation percentage between 9% and 1%, but such definition is rather arbitrary. For most of the time during data collection, the upper instrument rig (Rig 1) was located in the swash zone, the middle rig (Rig 2) was located in the transition zone and the lower rig (Rig 3) was located in the surf zone. Time series of water depth, crossshore current velocity and suspended sediment flux highlight some fundamental differences in the sediment transport processes in each of these zones (Fig. 5). The water motion in the surf zone is characterised by standing infragravity wave motion and shorewardpropagating bores. The cross-shore flow velocity is generally less than 1 m s 1, but this may be exceeded during strong offshore pulses associated with standing infragravity wave motion (Butt and Russell, 1999). Suspended sediment fluxes are modest, generally less than 1 kg m 1 s 1. In the transition zone, the water motion also results from the combination of standing infragravity wave motion and shoreward-propagating bores, but due to the reduced water depth, the beach is occasionally exposed. Strictly speaking, these longperiod events are swashes, but the individual bores that comprise them are still clearly discernible, Depth (m) Velocity (m s -1 ) Flux (kg m -1 s -1 ) SWASH ZONE Time (s) TRANSITION ZONE Time (s) SURF ZONE Time (s) Fig. 5. Concurrent time series of water depth, cross-shore current velocity (measured.3 m from the bed) and suspended sediment flux (integrated over the water column) measured by the three instrument rigs during high tide. Note that the scales of the vertical axes vary between the different instrument rigs.

7 G. Masselink et al. / Marine Geology 216 (25) especially in the pressure record. The cross-shore flow velocity in the transition zone frequently exceeds 1ms 1 and may reach 2 m s 1 during strong offshore pulses. Suspended sediment fluxes in the transition zone are at least one order of magnitude greater than in the surf zone, with individual bores moving sediment onshore while the infragravity motion induces strong offshore sediment fluxes. The water motion in the swash zone is driven by isolated swash events occurring at infragravity frequencies. Uprush and backwash velocities generally exceed 1 m s 1 and the duration of the uprush is commonly shorter than that of the backwash. Suspended sediment fluxes are similar to that in the transition zone and often exceed 1 kg m 1 s 1. Maximum sediment fluxes occur at the start and the end of the uprush and backwash, respectively. The tide-induced change in water level and horizontal shoreline position during the data collection period was.3 m and 2 m, respectively, which mean that the fixed instrument rigs were subjected to both surf and swash processes. The data collected by the three instrument rigs were divided into 2-min sections and time-averaged velocity statistics and suspended sediment fluxes were computed. Only data for which the water depth N.35 m were used, so sediment transport by the backwash is expected to be significantly underestimated. The data collected by each instrument rig were combined on the basis of the average water depth over the 2-min period (Fig. 6). In the intermittently exposed swash zone the average water depth has no real physical relevance, however, it is strongly correlated to the relative amount of time that a location in the swash zone is submerged. The transition zone represents the most energetic part of the nearshore region and is characterised by the largest cross-shore flow velocities and suspended sediment fluxes (shaded region in Fig. 6). The direction of the net suspended sediment flux varies between the different zones. Most swash events tend to move more sediment up the beach than down the beach and the net sediment flux in the swash zone is % Submergence mean u (m s -1 ) s.d. u (m s -1 ) 1 5 Rig 1 Rig 2 Rig h (m) on/off flux (kg m -1 ) total flux (kg m -1 ) net flux (kg m -1 ) h (m) Fig. 6. Percentage of time submerged, velocity statistics (mean and standard deviation of cross-shore flow velocity) and suspended sediment fluxes (onshore, offshore, total and net) computed using 2-min long data segments. The shaded rectangle represents the transition zone that separates the swash zone from the surf zone.

8 176 G. Masselink et al. / Marine Geology 216 (25) onshore (recall, however, that the backwash sediment transport is underestimated). In the transition zone, the net sediment flux is highly variable, but appears to be more offshore than onshore. The presence of a sediment transport divergence in the transition zone was also reported by Butt et al. (22b). In the surf zone, the net sediment flux is close to zero. 4. Hydrodynamics and sediment transport processes in the swash zone The data collected at Rig 1 were used to investigate sediment transport processes in the swash zone. Individual swashes, which start and end with nearzero water depth (b.15 m), were extracted from the water depth time series. From this data set, swash events with a duration longer than 15 s and a maximum swash depth in excess of.15 m were selected for further analysis. The resulting 3 swashes were all single events (i.e., no swash interactions), had a clear start and end, displayed no anomalous spikes, did not exhibit any sign of burial of the lowest OBS sensor and did not show any unexpected cross-shore flow reversals. The lower current meter measures flow velocities at a water depth of.3 m and the velocity record is therefore truncated at the end of the backwash. To compensate for the resulting underestimation of the water discharge and suspended sediment flux, it was assumed that the flow velocity at the end of the backwash is equal to the flow velocity averaged over the last second before truncation. This data extrapolation has no significant effect on the sediment transport results, because they only include swash depths in excess of.35 m. Table 1 lists some statistics of the swash events used in the analysis and also indicates the effect of extrapolating the flow velocity at the end of the backwash. For all events, the duration of the uprush is shorter than that of the backwash, while the timeaveraged swash velocity during the uprush is generally less than that during the backwash. The total swash discharge (product of swash velocity and depth integrated over the uprush/backwash duration) and the total suspended sediment flux (product of instantaneous swash discharge and vertically averaged suspended sediment concentration integrated over the uprush/backwash duration) are very similar for both phases of the swash flow if the backwash velocity data are extrapolated. If the backwash data are not extrapolated, however, the amount of sediment transport during the backwash appears significantly underestimated. Assuming that the flow velocities are correctly extrapolated up to the end of the backwash, about 25% of the suspended sediment transport during the backwash occurs when the water depth is less than.35 m. Each swash event was re-sampled to a normalised time scale t/t, where t is time and T is swash duration, using a sampling interval of.1. The re-sampled swashes were subsequently combined into an ensemble-swash event by averaging important properties, such as swash depth, flow velocity, suspended sediment concentration, suspended sediment flux, vertical pressure gradient in the bed, Reynolds number and Froude number (Fig. 7). Similar time series of a single event are also shown to illustrate the quality of the original data. The characteristics of the ensemble swash event compare well to that of the dexamplet swash event, suggesting that the former is a good representation of the average swash. The time series of swash properties for the ensemble and example swash event highlight fundamental differences between the uprush and backwash phases of the swash flow, emphasising that the latter is not the reverse of the former. The swash depth increases very rapidly at the start of the uprush, steadily decreases during the backwash, while remain- Table 1 Summary statistics for the 3 selected swash events Uprush Backwash to h=.35 m Backwash to h =.15 m Duration (s) 14.4 ( ) 21.7 ( ) 26.3 ( ) Mean velocity (m s 1 ).61 (.38.78).67 (.36.94).74 (.37.93) Discharge (m 3 m 1 ) 1.66 ( ) 1.46 ( ) 1.53 ( ) Flux (kg m 1 ) 68.2 ( ) 48.9 ( ) 64.7 ( ) Numbers between parentheses represent minimum and maximum values, respectively.

9 G. Masselink et al. / Marine Geology 216 (25) Fig. 7. Time series of swash depth h, flow velocity u at.3 m from the bed, suspended sediment concentration c averaged over the water column, total suspended sediment flux q, vertical pressure gradient dp /dz in the upper.2 m of the bed, Froude number Fr and Reynolds number Re for the ensemble swash event (left panels) and an example swash event (right panels). The shading in the top panels represents the suspended sediment concentration, ranging from less than 1 kg m 3 around the time of flow reversal, to 2 kg m 3 at the start of the uprush and the end of the backwash. The solid and dotted lines in the ensemble swash time series represent the mean of all swash eventsfone standard deviation. The vertical dashed lines indicate the time of flow reversal. The horizontal dashed line in the Froude number plots separates subcritical (Fr b1) from super-critical (Fr N1) flow conditions.

10 178 G. Masselink et al. / Marine Geology 216 (25) ing relatively constant over an extended period of time around flow reversal (t/t =.38; t =13 s). The flow velocity during the uprush decreases, whereas it increases during the backwash. Maximum uprush and backwash velocities are around 1.5 m s 1. Consistent with the predictions of a ballistic swash model (Hughes and Baldock, 24), but contrary to the findings of Puleo et al. (23), there is no evidence of a landward directed flow acceleration at the start of uprush. The temporal variation in the average suspended sediment concentration and total suspended sediment flux is strongly related to the swash velocity. Maximum near-bed sediment concentrations in excess of 1 kg m 3 occur at the start and end of the swash cycle, whereas the water is relatively clear at the time of flow reversal. Sediment fluxes are also maximum at the start and end of the swash cycle and are generally in excess of 1 kg m 1 s 1. Insignificant sediment fluxes occur over a relatively long period of time (t/t =.2.7; t =1 25 s) around flow reversal. The suspended sediment flux during the uprush is generally larger than during the backwash. Significant and consistent vertical pressure gradients are observed in the bed. At the start of the uprush, the pressure gradient is positive (ca. 1) for a brief period (potentially causing infiltration), whereas during the backwash the pressure gradient is considerably smaller ( b.5) and negative (potentially causing exfiltration). The variation in the Reynolds and Froude numbers over the swash cycle highlights a further fundamental difference between the uprush and backwash phase of the swash flow. Most of the sediment transport during the uprush occurs under sub-critical and highly turbulent flow conditions (Fr b 1 and Re N 1,), whereas that during the backwash takes place when the flow is super-critical and significantly less turbulent (Fr N1 and Re b1,). It is noted that Re in this context is related to wall-generated turbulence and not bore turbulence. The ensemble and dexamplet swash events shown in Fig. 7 suggest that the distribution of suspended sediment over the water column during the uprush is different to that during the backwash. As a first-order, heuristic approach to investigating the suspension process we will consider the vertical mixing of suspended sediment due to turbulent diffusion. The eddy viscosity of the water e and the eddy diffusivity of the sediment e s are usually defined by (Nielsen, 1992): quw P ¼ qe Bu ð1þ Bz P Bc ws c ¼ e s ð2þ Bz where q is the fluid density, u and w are the fluid velocities in the horizontal stream-wise and vertical directions, respectively, z is elevation above the bed, w s is the sediment fall velocity and c is the sediment concentration. The terms quw P and P w s c represent the vertical fluxes of momentum and sediment, respectively. It is often assumed that e and e s is independent of z and that e s ¼ ae, where the proportionality coefficient a is commonly assigned the value of 1 for fine sand (Dyer, 1986). Integrating Eq. (2) and assuming that e s is vertically invariant results in c z ¼ C e z=l s ð3þ where c z is the sediment concentration at a distance z from the bed, C is the reference sediment concentration at the bed (z =) and l s is a mixing length scale given by e s /w s. The sediment diffusion model described by Eq. (3) was used to investigate the difference in the suspended sediment concentration profiles between the uprush and backwash phases of the flow. For each selected swash event, the average suspended sediment concentration measured at z =.1,.2,.3,.4 and.5 m was computed for the two phases of flow. Only data when the swash depth was more than.65 m were considered to ensure that all elevations were equally represented. For each uprush and backwash, Eq. (3) was fitted to the data and average values for C and l s were computed (Table 2). The results indicate that the reference concentration during the uprush (C =13 kg m 3 ) is almost twice that during the backwash (C =71 kg m 3 ). The suspended sediment concentrations are not only higher during the uprush, but the sediment is also better mixed over the water column with the mixing length during the uprush (l s =.39 m) being almost twice that during the backwash (l s =.23 m). While the qualitative results of the steady-state approach just employed are realistic, the precise

11 G. Masselink et al. / Marine Geology 216 (25) Table 2 Results of fitting Eq. (3) to the suspended sediment profiles averaged over the uprush and backwash for the 3 selected swash events Uprush Backwash C (kg m 3 ) 13 (53 28) 71 (13 168) l s (m).39 (.21.65).23 (.16.32) r 2.95 (.86.99).97 (.9.99) Numbers between parentheses represent minimum and maximum values, respectively. magnitudes for the reference concentration C and the mixing length l s averaged over the uprush and backwash are not very representative, because C and l s are likely to vary with time. We have no a priori knowledge of their temporal variation, so again we employ a heuristic approach and investigate their temporal variation by fitting Eq. (3) to the suspended sediment concentrations at the five lowermost elevations (z =.1.5 m) at each normalised time step. The results of this analysis are shown in Fig. 8 together with the results obtained for the dexamplet swash event. (The ensemble swash event shown in Fig. 8 is different from that shown in Fig. 7, because different water depth cut-offs were used:.65 m for Fig. 8 and.35 m for Fig. 7.) The temporal variation in reference concentration is very similar to the average suspended sediment.2 ENSEMBLE SWASH EVENT.2 EXAMPLE SWASH EVENT h (m) u (m s -1 ) C o (kg m -3 ) l s (m) r t/t t (s) Fig. 8. Time series of swash depth h, flow velocity u at.3 m from the bed, reference concentration C, mixing length l s and the coefficient of determination r 2 between observations and the diffusion model (Eq. (3)) for the ensemble swash event (left panels) and an example swash event (right panels). The vertical dashed lines indicate the time of flow reversal. C and l s are only plotted if the associated r 2 value exceeds the 95% confidence interval for zero correlation (r 2 N.78).

12 18 G. Masselink et al. / Marine Geology 216 (25) concentrations, displaying a maximum at the start of the uprush and the end of the backwash (C c2 kg m 3 ), and low concentrations around flow reversal (C c25 kg m 3 ). The mixing length is also maximum (l s =.3.7 m) at the start of the uprush (t/t =.1; t = 4 s), but rapidly decreases to l s c.2.3 m over the remainder of the swash cycle. The correspondence between Eq. (3) and the data is poor at the start of the uprush (r 2 b.9). Further inspection of the data reveals that the lowest two, and sometimes three, OBSs are saturated at the start of the uprush, recording a near-constant value of around 2 kg m 3. The suspended sediment concentrations close to the bed are therefore underestimated, and may have resulted in an underestimation of C, an overestimation of l s and low r 2 values. Alternatively, the front of the leading edge of the swash lens involves some larger scale turbulence left over from bore collapse that results in a convective-style of sediment suspension that is poorly described by the diffusion model (cf., Nielsen, 1992). For the remainder of the swash cycle, however, r 2 values are consistently higher than.9, and the diffusion model appears reliable. This is despite the shortcomings of assuming a steady e and e s that are independent of z. Values for l s over the latter part of the uprush and during the backwash are similar to those found for plane bed surf zone conditions (e.g., Black and Rosenberg, 1991; Osborne and Greenwood, 1993; Masselink and Pattiaratchi, 2). Assuming a sediment fall velocity of w s =.4 m s 1 and a mixing length of l s =.25 m, the resulting sediment mixing coefficient e s is.1 m 2 s 1. If we accept the common assumption that the proportionality coefficient a between the sediment diffusivity and eddy viscosity is unity, then the eddy viscosity e is also.1 m 2 s 1, which compares reasonably well with values reported for the surf zone (e.g., Black et al., 1995 found a value of.3 m 2 s 1 ). Field measurements of incident-swash motion demonstrate that the turbulent boundary layer under swash is well developed and that the vertical structure of the cross-shore orbital velocities is approximately logarithmic within.5 m from the bed (Raubenheimer et al., 24). The boundary layer thickness associated with the infragravity-swash motion investigated here is expected to be at least as large. The velocity profile within a logarithmic boundary layer can be described by u z ¼ u 4 j ln z ð4þ z where u z is the velocity at a distance z from the bed, u T is the shear velocity, j is von Karman s constant (equal to.4 for unstratified flow) and z is the hydraulic bed roughness length. The shear velocity is related to the bed shear stress s and the water density q by s ¼ qu 2 4 ð5þ and can be derived from the velocity profile in the logarithmic boundary layer. Two velocity measurements made at different elevations within the boundary layer are sufficient to determine the bed shear stress s ¼ q j u 2 u 2 1 ð6þ lnðz 2 =z 1 Þ where u 1 and u 2 are the velocity measured at z 1 and z 2 from the bed, respectively, and z 1 bz 2. An alternative way to calculate the bed shear stress from flow velocity data is s ¼ :5qfu 2 ð7þ where u is the free-stream velocity outside the logarithmic boundary layer and f is a friction factor. Swash velocities measured at.3 and.6 m from the bed were used with Eq. (6) to estimate the variation in bed shear stress over the swash cycle, under the assumption that both velocity measurements were from within the boundary layer. This assumption can, at least in part, be justified on the basis of the temporal evolution of the suspended sediment concentration profile (Fig. 7). During the time that the majority of the suspended sediment transport takes place (t/t b.2 during uprush and t/t N.7 during backwash), significant amounts of sediment are suspended into the water column more than.5 m from the bed, suggesting that the top of the boundary layer is at least the same distance from the bed. The temporal variation in s was computed for the ensemble swash event and the results are shown in Fig. 9. The results obtained using the dexamplet

13 G. Masselink et al. / Marine Geology 216 (25) ENSEMBLE SWASH EVENT.2 EXAMPLE SWASH EVENT h (m) u (m s -1 ) du/dz (s -1 ) tau (N m -2 ) t/t t (s) Fig. 9. Time series of swash depth h, flow velocity u at.3 and.6 m from the bed (solid and dashed line, respectively), velocity gradient du/ dz and bed shear stress s for the ensemble swash event (left panels) and an example swash event (right panels). Boundary layer parameters du/ dz and s were computed using Eq. (6) and results are only shown if u at.6 m from the bed is larger than u at.3 m from the bed. The vertical dashed lines indicate the time of flow reversal. swash event are again included for comparison. Except at the very start of the uprush (t/t =.3; t =.5 s) and at around the time of flow reversal, the velocity measured at z =.6 m is consistently larger than that measured at z =.3 m. Vertical shear is considerable during swash motion and the velocity gradient at the start of the uprush (du/dzc1 s 1 )is approximately twice that at the end of the backwash (du/dzc5 s 1 ). The combination of a steeper velocity gradient and larger flow velocity results in considerably larger bed shear stress at the start of the uprush (s c25 N m 2 ) than at the end of the backwash (s c1 N m 2 ). 5. Modeling sediment transport processes in the swash zone There is no generally accepted approach to modeling sediment transport (Butt and Russell, 2; Elfrink and Baldock, 22), and to date, the only model tested in the swash zone is the energetics-based model of Bagnold (1963, 1966). The applicability of this model has been investigated using various types of data by Hughes et al. (1997a), Masselink and Hughes (1998), Puleo et al. (2), Masselink and Li (21) and Evans et al. (23). The general conclusion of this work is that although the energetics equations describe the sediment transport rates reasonably well, there are some fundamental problems with this approach. Most important are the presence of different calibration coefficients for the uprush and backwash, and the fact that the transport efficiency factors appear to be unrealistically high (Puleo et al., 2). Here, we draw from the steady flow sediment transport literature and assume that the non-dimensional sediment transport rate / is proportional to the Shields parameter h according to (Meyer-Peter and Muller, 1948) / ¼ kðh h c p Þ ffiffiffi h ð8þ where k is a calibration coefficient (k = 8 in the classical bedload formula) and h c is the critical

14 182 G. Masselink et al. / Marine Geology 216 (25) Shields stress parameter below which no sediment transport takes place (h c c.5). For convenience, the effect of a sloping bed (tan bc.15) is ignored. The non-dimensional transport rate / is related to the mass transport rate q by q / ¼ s q pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D 5 ðs 1ÞgD 5 and the Shields parameter h is given by ð9þ s h ¼ ð1þ qðs 1ÞgD 5 where s is the relative density of the sediment (s =q s /q, where q s and q are the densities of sediment and water, respectively), g is the gravitational acceleration and D 5 is the median sediment size. The bed shear stress s in Eq. (1) can be determined directly from the velocity profile (Eq. (6)) or estimated using the friction factor (Eq. (7)). According to this approach, the sediment transport rate is approximately proportional to the velocity cubed ( q ~ u 3 ), which is similar to the bedload component of Bagnold s energetics equation. The applicability of Eq. (8) was investigated using the velocity and suspended sediment flux data from the 3 selected swash events discussed previously. Data for which the water depth was less than.35 m were excluded from the analysis, because the flow velocity and suspended sediment flux for such shallow flows was not measured, but extrapolated. The Shields parameter was computed with Eqs. (7) and (1), using the velocity measured at.3 m from the bed and a friction factor of f =.3 (this value was chosen because it resulted in comparable values for s computed using Eqs. (6) and (7)). Regression analysis reveals that the sediment transport model (Eq. (8)) based on the Shields parameter works rather well, in particular for the backwash phase of the swash flow (Fig. 1). In agreement with previous swash zone sediment transport studies (Masselink and Hughes, 1998; Puleo et al., 2; Masselink and Li, 21), the calibration coefficient for the uprush (k = 16.4) is significantly larger than that for the backwash (k =11.3). There are two problems with the above approach. First, to estimate the bed shear stress using Eq. (7) requires the free-stream flow velocity, whereas the present velocity data are clearly collected from within the boundary layer (Fig. 9). Even if free-stream velocity data were available, converting these to bed shear stress estimates involves knowledge of the friction factor. Reported values for f vary widely and it is not even clear whether f during the uprush is the same as during the backwash (cf., Raubenheimer et al., 24; Conley and Griffin, 24). Second, relating the suspended sediment flux q to the Shields parameter h is statistically unsound, because the flow velocity u occurs in both sides of the equation: q ~u and h ~u 2. In other words, statistically significant correlations between q and h will be found, regardless of whether the two parameters are causally related. A more physically sound way of testing the sediment transport model based on the Shields parameter is to use the bed stress derived from the 8 6 UPRUSH BACKWASH 4 φ = 16.4 (θ.5) θ.5 ; r 2 =.71 φ = 11.3(θ.5) θ.5 ; r 2 =.86 3 φ 4 φ θ θ Fig. 1. Scatter plots of non-dimensional suspended sediment flux / versus the Shields parameter h for the 3 selected swash events for the uprush (left panel) and backwash (right panel). The dashed line represents the line-of-best fit for the sediment transport model represented by Eq. (8).

15 G. Masselink et al. / Marine Geology 216 (25) velocity profile using Eq. (6), rather than assuming it is proportional to u 2 according to Eq. (7) and dhidet the friction factor within the calibration coefficient. Ideally, one would want to extract a time series of the bed shear stress from the swash velocity data and relate this to the instantaneous suspended sediment transport rate. The swash flow is highly turbulent, however, and spatially incoherent velocity fluctuations significantly compromise the derivation of the instantaneous bed shear stress from the velocity profile (refer to the s time series of the example swash event in Fig. 9). Averaging removes these problematic fluctuations and therefore the ensemble swash event is used here. The variation in h over the ensemble swash cycle was obtained from the s time series and Eq. (1). The results of least-squares fitting Eq. (8) to the ensemble swash data are shown in Fig. 11. The measured suspended sediment flux is predicted very well by the model and most importantly, there does not seem to be any need for having different k-values for the uprush and backwash. This would imply that the difference in k-values between the uprush and the backwash in previous applications of the energetics-based model is due at least in part to differences in the friction factor between uprush and backwash. Perhaps fortuitously, the calibration coefficient obtained for the swash zone data (k =15) is only slightly higher than that obtained by Nielsen (1992, p. 113) for total load transport rates under steady flows over upper-stage plane beds (k = 12) (Fig. 11). 6. Discussion Detailed measurements of hydrodynamics and suspended sediment transport are reported from the swash zone of a sandy, dissipative beach. The data discussed here are from a single high tide, but additional analysis using data collected during other wave/tide conditions has been reported elsewhere (Evans, 24). The results of this earlier analysis were similar to those presented here. It must be emphasized, however, that the results of this investigation are considered representative only of infragravity swash motion they are not necessarily applicable to beaches dominated by incident swash at wind and swell wave frequencies. An important result of this field study is the presence of a relatively well-developed boundary layer in the mid-swash zone throughout the swash cycle, as indicated by a significant difference in the flow velocities recorded at.3 and.6 m from the bed. The velocity data demonstrate that the swash boundary layer is at least.3 m thick, except perhaps around the time of flow reversal. Considering the long duration of these swash events and recent field results reported by Raubenheimer et al. (24), it seems likely that the boundary layer is at least.6 cm thick. It is important to highlight the difficulties with measuring this type of process within an Eulerian reference frame (i.e., with fixed instrument locations). The dbirtht of the uprush boundary layer occurs with bore collapse at the seaward end of the swash zone, φ= 15. (θ.5)θ.5 ; r 2 =.94 φ = 15. (θ.5)θ.5 measurements 3 φ 2 φ 2 1 uprush backwash θ Normalised time Fig. 11. Scatter plot of non-dimensional suspended sediment flux / versus the Shields parameter h for the ensemble swash event (left panel). The dashed line represents the line-of-best fit for the sediment transport model represented by Eq. (8). Comparison between measured and predicted non-dimensional suspended sediment flux / over the ensemble swash cycle (right panel). The vertical dashed line indicates the time of flow reversal.

16 184 G. Masselink et al. / Marine Geology 216 (25) and as the swash lens climbs the beach the boundary layer grows. At flow reversal, the uprush boundary layer disappears and the backwash boundary layer develops as the water moves back down the beach. The thickness of the measured boundary layer therefore depends on the distance of the instruments from the seaward end of the swash zone (Fig. 12). In the lower swash zone the uprush boundary layer will be relatively dyoungt (thin), whereas in the upper swash zone it will be more dmaturet (thick), and vice versa for the backwash. If the swash excursion is large, such as in the case of infragravity swash motion, the swash boundary layer has ample time to attain a much greater thickness than that under waves. The conceptual development of the swash boundary layer shown in Fig. 12 is inferred from velocity time series such as those shown in Panels A and B. The velocity time series recorded at.3 and.6 m from the bed at the seaward end of the swash zone show very limited shear during the uprush and a pronounced velocity gradient at the end of the backwash. At the mid-swash position, however, significant shear is present during both phases of the swash flow. As a further indication of the variation in boundary layer development, the average shear was computed for the onshore and offshore phases of the flow using data from all three rigs. Only data for which the velocity at both.3 and.6 m from the bed exceeded.5 m s 1 were used. The average velocity shear at Rigs 2 and 3 was comparable and similar for the onshore and offshore phase of the flow (bdu /dz N=3 4 s 1 ). For Rig 1, on the other hand, the average shear during the onshore flow ( b du / dz Nc9 s 1 ) was significantly greater than that during the offshore phase of the swash flow (bdu / dz N c4 s 1 ). Recent laboratory measurements of swash zone hydrodynamics have suggested that breaking-waveinduced (bore) turbulence dominates during the uprush, while bed-generated (wall) turbulence is more important during the backwash (Petti and Longo, 21; Cowen et al., 23). If this turbulence impinges on the bed, it will contribute to the bed shear stress and therefore sediment transport (Puleo et al., 2). The role of turbulence is certainly significant in the transition zone, where a mixture of swash and surf zone bores operate. Inspection of the data from this region reveals that the onshore suspended sediment flux associated with shoreward-propagating bores depends strongly on the water depth in front of the bore, rather than the actual flow velocity in the bore. It is probable that for bores traveling in shallow water, a significant proportion of the bore-generated turbulence is affecting the bed, enhancing the local bed shear stress, and hence sediment transport. The effect of bore-generated turbulence in our results obtained from the mid-swash zone is expected to be rather limited, however, due to the long swash periods (N15 s) and large swash excursions (N2 m). After a turbulent bore collapses at the start of the swash zone, wave breaking ceases and bore turbulence is no longer generated. The bore turbulence will then decay quite rapidly, for example, comparisons between the production and dissipation of turbulent kinetic energy associated with a hydraulic jump indicates that once the turbulence leaves the production region at the front, it is dissipated within a limited region of a few times the height of the jump (Rouse et al., 1958). Estimates of turbulent kinetic energy (TKE) based on field measurements made in an infragravity-dominated swash zone by Osborne and Rooker (1999) also suggest that the role of bore turbulence may be limited. Their data demonstrate similar levels of TKE during the start of the uprush and the end of the backwash, implying that the TKE is due to wall, rather than bore turbulence. Bore turbulence may indirectly affect the uprush by suspending sediments during bore collapse, which are then advected up the beach by the uprush (Jackson et al., 24; Pritchard and Hogg, 25). Again, such an indirect impact of bore turbulence is unlikely to have been important in the present study, because the distance between the region of bore collapse and the mid-swash zone would have enabled the bore-collapse-entrained sediment to have settled to the bed prior to arriving at the mid-swash position. The vertical velocity gradient between.3 and.6 m from the bed was inserted into Eq. (6) to derive the bed shear stress under the assumption that both velocity measurements were collected from the turbulent boundary layer. The results demonstrate that the bed shear stress and consequently the inferred friction factor during the uprush is approximately twice that during the backwash, which is consistent with two previous studies (Cox et al., 1998; Conley and Griffin, 24). A field study by Raubenheimer et