cross-shoresuspendedsedimenttransportinthesurfzone: a¢eld … · 2005-03-22 · existing...

Cross-shore suspended sediment transport in the surf zone:a ¢eld-based parameterization

Troels Aagaard a;�, Kerry P. Black b, Brian Greenwood c

a Institute of Geography, University of Copenhagen, Oster Voldgade 10, DK-1350 Copenhagen K., Denmarkb ASR Ltd., Marine and Freshwater Consultants, P.O. Box 13048, Hamilton, New Zealand

c Department of Geography, The University of Toronto at Scarborough, 1265 Military Trail, Scarborough, ON, Canada M1C 1A4

Received 21 June 2001; accepted 4 February 2002

Abstract

Existing cross-shore sediment transport models for two-dimensional surf zone bathymetries almost invariablypredict offshore-directed sand transports and bar migrations during storm conditions. However, onshore-directedsuspended sediment fluxes and associated nearshore bar migration were observed during recent field experiments on agently sloping beach on the Danish North Sea coast. Field measurements of suspended sediment flux obtained duringthree experiments on two different beaches are used to parameterize the observed fluxes. This parameterizationpredicts suspended sediment transport due to incident waves and undertow across bars in two-dimensional surf zones.First, a non-dimensional sediment flux index is formulated which describes the tendency towards net onshore oroffshore transport and the strength of that tendency. The non-dimensional formulation circumvents the problem ofmeasurement inconsistencies due to varying elevations of sediment concentration sensors relative to the bed. Theindex is found to depend upon the undertow velocity, the incident wave skewness and the cross-correlation betweenorbital velocity and sediment concentration. However, some of these parameters are difficult to predict, particularly inbarred surf zones and therefore, the independent variables are recast in terms of a set of more easily obtainableparameters. The sediment flux index depends on a combination of the following: non-dimensional bed shear stress(the Shields parameter), relative water depth, wave orbital velocity, relative wave height and bed slope. Finally, aformulation of suspended sediment transport across bars is obtained by linking the flux index with a parameterizationof the sediment concentration/distribution in the water column. These concentrations are found to depend on non-dimensional bed shear stress, relative wave height and water depth. The formulation predicts a tendency for onshore-directed sediment transport due to incident waves on gently sloping beaches and/or with large bed shear stresses. Onsteeply sloping beaches and/or in the inner part of the surf zone there is a tendency towards offshore sedimenttransports due to the undertow. 6 2002 Elsevier Science B.V. All rights reserved.

Keywords: sediment transport; sediment concentrations; incident waves; undertow; morphodynamics; beach processes

1. Introduction

Considerable e¡ort has been spent within coast-al science and engineering towards predicting thedirection and magnitude of sediment transport in

0025-3227 / 02 / $ ^ see front matter 6 2002 Elsevier Science B.V. All rights reserved.PII: S 0 0 2 5 - 3 2 2 7 ( 0 2 ) 0 0 1 9 3 - 7

* Corresponding author. Fax: +45-3532-2501.E-mail address: [email protected] (T. Aagaard).

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Marine Geology 185 (2002) 283^302

www.elsevier.com/locate/margeo

the surf zone, and the ensuing morphological re-sponse. While relatively robust models exist forthe prediction of longshore sediment transport,this is not the case for the cross-shore componentwhich is generally responsible for beach pro¢lechange. A major reason for this lack of predictivecapability is that several mechanisms contributeto the transport, including mean currents and os-cillatory waves at incident and infragravity fre-quencies (e.g. Osborne and Greenwood, 1992;Aagaard and Greenwood, 1994; Ruessink et al.,1998; Aagaard et al., 1998; Russell and Huntley,1999). The relative importance and directional at-tributes of these components will determine themagnitude (and direction) of the net transport.There is a general consensus that in cases whenwaves are breaking, the sediment transport tendsto be directed o¡shore, due to the seaward-di-rected undertow generated by wave breakingand radiation stress decay. The ensuing pro¢leresponse is a seaward migration of nearshorebars. During non-breaking wave conditions, thetransport is assumed to be onshore-directed, dueto the e¡ects of incident wave skewness/asym-metry driving nearshore bars landward (e.g. She-pard, 1950; Birkemeier et al., 1997; Komar, 1998;Lee et al., 1998; Elgar et al., 2001).Osborne and Greenwood (1992) attempted to

parameterize suspended sediment transport direc-tions in the ¢eld using local values of the relativewave height (Hs/h, where Hs is signi¢cant waveheight and h is water depth), while Ruessink etal. (1998) used an extensive data set to concludethat the net sediment transport direction in thenearshore indeed appeared to be a function ofHs/h. Under non-breaking conditions, transportrates were small, while breaking waves (Hs/hsW0.33) induced a signi¢cant o¡shore-directednet transport due to both undertow and group-bound long waves.A fairly large number of numerical models and

algorithms exist for prediction for cross-shoresediment transport in two-dimensional bathymet-ric settings. Tests of the Bailard energetics model(Bailard, 1981) using measured velocity time series(Thornton et al., 1996; Gallagher et al., 1998) ortime-averaged quantities of velocity moments(Russell and Huntley, 1999) yield predictions of

o¡shore sediment transport landward of thebreakpoint and onshore transport outside thebreakpoint. Landward of the breakpoint, theSBEACH model (Larson and Kraus, 1989) pre-dicts o¡shore-directed sediment transport due tothe undertow, if wave dissipation is larger thansome critical value, and zero transport otherwise.Surf zone sediment transport directions and ratespredicted by the CROSMOR model (Van Rijn,1993, 1998) depend on a balance between pre-dicted undertow velocity and higher-order veloc-ity moments and generally produces o¡shore-di-rected transports and o¡shore bar migrationlandward of the wave breakpoint (Grasmeijer etal., 1999; Van Rijn et al., 1999). Field tests re-vealed a tendency towards overpredicting waveskewnesses and undertow velocities in the surfzone (Grasmeijer and van Rijn, 1999). A commoncharacteristic of these models is that they assumea zero lag between wave orbital velocity and near-bed sediment concentration and they predict fairlywell o¡shore-directed sediment transport ratesdue to the undertow in the case of breakingwaves, whereas there are di⁄culties with predict-ing the (necessary) onshore-directed transportsunder non-breaking (or breaking) wave condi-tions (Schoonees and Theron, 1995; Thornton etal., 1996; Miller et al., 1999). Recently, someprogress may have been made using a phase-re-solving intra-wave model (Rakha et al., 1997)which seems to be able to yield realistic on-shore-directed transports outside laboratory surfzones and also at some locations inside the break-er zone. This model is, however, rather compli-cated and di⁄cult to apply.Hence, a general characteristic of these param-

eterizations and models is that they, perhaps ex-cept for the latter reference, consistently predicto¡shore-directed sediment transports and near-shore bar migration within the surf zone. Thismay cause problems when they are applied tonatural surf zones. One problem is that surfzone morphology in the ¢eld may be stronglythree-dimensional with crescentic bars and hori-zontally segregated mean £ows involving rip cur-rents. Such conditions can introduce strong mor-phodynamic feedbacks between the morphologyand the hydrodynamics; in this case the pro¢le

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T. Aagaard et al. / Marine Geology 185 (2002) 283^302284

response displays a spatial variability and barsfrequently move onshore even under breakingwave conditions (Greenwood and Davidson-Ar-nott, 1979; Wright and Short, 1984; Aagaard etal., 1998; Ruessink and Terwindt, 2000). Fur-thermore, even in the case of a two-dimensionalbathymetry, i.e. with straight shore-parallel near-shore bars and a vertically segregated mean cur-rent (undertow) circulation and thus under con-ditions when the models would be expected toapply, bars within a high-energy surf zone havebeen observed to move onshore during intensestorms, driven by landward-directed suspendedsediment £uxes at incident wave frequencies (Aa-gaard and Greenwood, 1999). Such onshore-di-rected sediment transports under breaking waveswere also observed by Ruessink et al. (1998) andMiller et al. (1999), but not explained.The present study was motivated by the obser-

vations of divergent sediment £ux directions andmorphological behavior under seemingly similarwave energy conditions on two di¡erent beacheson which the mean current circulation was char-acterized by vertically segregated mean £ows. Inorder to attempt a reconciliation of these con£ict-ing observations, the present paper proposes anempirical process-based formulation of cross-shore suspended sediment transport under break-ing waves for two-dimensional bathymetries.Field data were collected from three experi-

ments on two distinctly di¡erent beaches andunder a wide range of incident wave energy con-ditions (breaker heights HbW0.2^2.8 m). First, anon-dimensional cross-shore sediment £ux indexis formulated, indicating the direction of the netsediment £ux close to the bed. This index isshown to depend upon a number of hydrodynam-ic and sediment dynamic process parameters thatare di⁄cult to predict a priori. The process pa-rameters are therefore recast in terms of a set ofhydrodynamic, textural and bathymetric proper-ties in order to obtain a parameterization of thedirectional characteristics of the sediment £ux inthe near-bed layer. Then, sediment concentrationsin the near-bed layer are parameterized using thesame ¢eld data sets and ¢nally combined with the£ux direction index to obtain a ¢rst approxima-tion of cross-shore near-bed sediment transport

rates across nearshore bars under breaking waveconditions.

2. Field sites

Field work was conducted on two distinctlydi¡erent beaches in terms of pro¢le con¢guration.The Skallingen ¢eld site is located on the DanishNorth Sea coast. It is a dissipative beach exposedto wind-generated waves from predominantlysouthwesterly and westerly directions. Fetchesare relatively long and during storms, o¡shorewave heights may exceed 5 m, with peak spectralperiods of 10^13 s. Low-energy swell may persistfor a couple of days after storms and the meanannual signi¢cant wave height is on the order of0.5^0.6 m.The nearshore is gently sloping (LW0.007) with

an intertidal slope of LW0.02^0.03. The meangrain size in the surf zone is 150^200 Wm andthe cross-shore pro¢le exhibits two to three sub-tidal (nearshore) bars as well as a highly mobileintertidal (swash) bar, see Fig. 1. During high-en-ergy events, depth-limited wave breaking usuallycommences some distance seaward of the barsand persists continuously from the middle bar tothe shoreline. The beach experiences a low-meso-tidal regime with a spring tidal range (TR) ofabout 1.8 m. The gentle slopes (horizontal shore-line excursion at spring tides: TR/LW75 m), andthe fact that the site is frequently subjected tostorm surges, enhance the e¡ects of water level£uctuations. Moderate storms typically result insurges of M 0.5 m, depending on wind direction,while severe (onshore) storms may elevate astro-nomically predicted tide levels by up to 3 m.Data from two ¢eld experiments at Skallingen,

which were conducted in the fall of 1995 and 1996are included here. During the ¢rst part of the1995 experiment (SK95), the morphology wascharacterized by almost straight bars dissectedby rip channels and distinct horizontally segre-gated cell circulations occurred (Aagaard et al.,1998). During the latter part of SK95 as well asduring the 1996 experiment (SK96), bars weretwo-dimensional and vertically segregated o¡-shore-directed mean £ows (undertows) occurred

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T. Aagaard et al. / Marine Geology 185 (2002) 283^302 285

whereas rip currents were absent. Only data fromthese two-dimensional bathymetric situations withan undertow circulation are considered in this pa-per and these are the conditions that most sedi-ment transport/morphodynamic models attemptto simulate.The second ¢eld site was the modally intermedi-

ate-state beach at Staengehus on the north coastof Zealand, Denmark. The site is exposed towardsthe northwest and the wave climate at the localityis highly variable. As the beach faces into thedirection of the strongest winds and fetches arerelatively short (9 150 km), brief storm eventswith breaker heights over the outer bar up to2^2.5 m and peak spectral wave periods of 5^7 sare interspersed with lengthy and relatively calmperiods. Long-period swell energy is insigni¢cant.The beach is virtually tideless with spring tidalranges of the order of 0.2^0.3 m. Surges up to0.5 m occur during lengthy northwesterly storms.The slope of the nearshore at Staengehus is

twice as steep as at Skallingen (LW0.016) andexhibits three nearshore bars (Fig. 1). Bar reliefis signi¢cantly larger than at Skallingen andwaves tend to reform in troughs between barseven under storm conditions. The mean sandgrain size on the bars is typically 200^250 Wmwhile the sand has been winnowed away andgravels and boulders are exposed in the troughsbetween bars. During the ¢eld experiment con-ducted during the fall of 1998, the two innerbars were weakly crescentic, but no rip circula-tions were observed at any time.

3. Instrumentation

Measurements at the two sites consisted ofwaves, currents and sediment £uxes being re-corded in cross-shore transects across the innernearshore zone, using arrays of electromagneticcurrent meters (Marsh McBirney OEM512), pres-sure sensors (Viatran Model 240) and opticalbackscatter sensors (DpA Instruments OBS-1P).Five/six and eight instrument stations were used,respectively, at Skallingen and at Staengehus(Fig. 2). Instruments were mounted on H-frameswith the sensors (except for the pressure trans-ducers) being suspended from the cross-pieces ofthe frames. The horizontal distance between thecurrent meters and the backscatter sensors wasapproximately 0.25 m.

Fig. 1. Cross-shore pro¢les at Skallingen (solid line) and atStaengehus (dashed line). DNN is Danish Ordnance Datum.

Fig. 2. Cross-shore pro¢les of the inner nearshore during thethree ¢eld experiments at Staengehus (STG98) and Skallingen(SK95, SK96). Sensor locations and instrument station desig-nations are indicated. Only stations mentioned in the texthave been shown.

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The optical backscatter sensors were deployedat nominal elevations of z=0.05, 0.10 and 0.20 m,and current meters were mounted at z=0.20^0.30m. While the OBS were deployed as close to thebed as possible to capture signi¢cant sedimentsuspensions, the current meters were kept furtheraway in order to minimize the risk of burial orsignal distortion from the boundary. At Skallin-gen, instrument elevations were recorded and ad-justed at each low tide, whenever possible, tocompensate for bed level changes. Between lowtides, sensor elevation was interpolated. At Staen-gehus, the surf zone was inaccessible during peri-ods of high energy and sensors could not be ad-justed. However, at stations S2 and S3 (Fig. 2),bed elevation sensors (Ridd, 1992; Aagaard et al.,2001) were installed approximately 1 m awayfrom the backscatter array. These sensors contin-uously recorded the elevation of the bed such thata rough estimate of OBS and current meter ele-vations at these positions could be obtained.All sensors were hardwired to shore-based data

acquisition systems and sampled at 4 Hz (10 Hz)for 34.1 (45) min at Skallingen (Staengehus) witha duty cycle of 1 h during storm events. Pressuresensors and current meters were calibrated priorto deployment. Field o¡sets were checked repeat-edly in buckets and during still water conditions.The optical backscatter sensors were gain-cali-brated in a recirculating tank after the experi-ments using sand from the deployment locations,while ¢eld o¡sets due to more or less permanentlysuspended organics and/or silt and clay particleswere determined for individual records using the¢fth percentile frequency output voltage (see Aa-gaard and Greenwood, 1994). Finally, sedimentsamples were taken at all instrument stations forsubsequent laboratory analysis and determinationof grain size parameters.

4. Data analysis

Instrument outputs were screened and inspectedvisually to check data quality. Noisy and/or erro-neous data e.g. due to instrument proximity to thebed, or burial were dismissed from further analy-

sis. At Staengehus, seaweed was a frequentproblem that manifested itself as large increasesin, or saturation of OBS signals for lengthy peri-ods of time. Current meters were also occasionallya¡ected by this problem, resulting in signi¢cantlydecreased sensor outputs usually occurring simul-taneously with backscatter problems. Records con-taining evidence of such problems were also dis-carded.Surface elevation spectra were computed from

pressure records and corrected for frequency-dependent depth attenuation using linear wavetheory over the frequency range 0^0.5 Hz. Dueto ampli¢cation of noise at high frequencies, anupper limit frequency cut-o¡ was determined as:

g c ¼ 0:564Zðg=dÞ0:5 ð1Þ

(Green, 1999) where g is radian frequency (2Z/T),g is the acceleration due to gravity and d is depthof submergence of the pressure sensor. Root-mean-square (rms) wave heights were computedas:

Hrms ¼ffiffiffi8

p Xg c

0

Ssðf Þ !0:5

ð2Þ

where Ss is surface elevation spectral density andsigni¢cant wave heights were determined asHs =

ffiffiffi2

pHrms. Wave heights at stations lacking

pressure sensors were estimated from current me-ter variance using the linear transfer function:

Hrms ¼ffiffiffi8

pð6c

2sh=gÞ0:5 ð3Þ

where c2 is velocity variance and h is water depth.The magnitude and skewness of wave orbital

velocities are generally considered to be of criticalimportance to the direction and magnitude of theincident wave-driven sediment £ux (e.g. Bailard,1981; Thornton et al., 1996; Gallagher et al., 1998;Van Rijn, 1998). Oscillatory velocities were de-meaned and separated into infragravity and inci-dent wave band contributions using Fourier ¢lter-ing techniques and a separation frequency of0.067 Hz. Cross-shore incident wave skewness

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was quanti¢ed by:

S ¼ ðu3c3u3t Þðu3c þ u3t Þ

ð4Þ

(Van Rijn, 1993; Aagaard and Greenwood, 1999)where uc, ut are the high-pass ¢ltered maximumoscillatory velocities at wave crests and wavetroughs, respectively. In the present data set, in-cident wave skewnesses were always positive, i.e.directed landward.In the calculations of suspended sediment

£uxes, data from bar crests and the upper sea-ward slopes of the bars were selected for analysis.This is where wave energy levels and consequentlybed shear stresses are the largest, generally result-ing in the largest sediment concentrations andgross (but not necessarily net) transport rates(e.g. Aagaard et al., 1998; Ruessink et al., 1998).Furthermore, vortex ripples which complicate thephase relationships between velocity and concen-tration (Osborne and Greenwood, 1993) are ab-sent at times of high energy. Finally, cross-shoretransport at such positions should re£ect the mi-gration of bars and thus the general morpholog-ical evolution of the pro¢le. Data from S2 (Skal-lingen) and S2, S3, S6 and S7 (Staengehus), seeFig. 2, have been selected for the sediment trans-port analysis.The present analysis is generally restricted to

the e¡ects of incident waves and mean currents,and sediment £uxes due to oscillatory infragravitymotions were ignored. Infragravity wave £uxesdisplay spatially and often temporally varying di-rectional characteristics in the surf zone (Aagaardand Greenwood, 1994; Thornton et al., 1996;Gallagher et al., 1998) and at the instrument lo-cations selected they contributed less than 20% ofthe gross sediment £ux, on average (Aagaard andGreenwood, 1999). Only at station S7 (Staenge-hus) did their contribution sometimes exceed 30%during an individual run. Such ratios are signi¢-cantly smaller than values obtained close to theshoreline/in the intertidal zone (e.g. Beach andSternberg, 1991; Russell, 1993; Aagaard, 2001)but agree with ratios reported by Ruessink et al.(1998) for positions in the nearshore.Finally, only data obtained under surf zone

conditions were used. The o¡shore extent of thesurf zone was determined from the local values ofthe relative wave height. Visual observations andwave height records from these two sites indicatethat wave breaking is initiated for a local relativewave height of Hs/hv 0.35 and most waves breakfor Hs/hv 0.40. Wave heights saturate for Hs/hW0.60 (e.g. Thornton and Guza, 1982; Wrightet al., 1982; Sallenger and Holman, 1985) andhere, this value has been used to separate the in-ner and the outer surf zones.Net suspended sediment £ux at a point was

computed as the cross-product of instantaneousvelocity (u) and sediment concentration (c) :

Gqsf ¼1n4uc ð5Þ

where n is the number of data points in the sam-ple and Gf denotes the time average. FollowingJa¡e et al. (1984) and Huntley and Hanes (1987),the net £ux was separated into a mean and anoscillatory term:

Gqsf ¼ u c þ u0c0 ð6Þ

where the ¢rst term on the right-hand side of theequation is suspended sediment £ux due to meancurrents which was always negative, i.e. directedo¡shore for the present data set. The second termin Eq. 6 is the £ux coupling (i.e. the covariance)between oscillatory wave motions and sedimentconcentration. This term was generally positiveat incident wave frequencies, i.e. onshore-directed.Information on transport magnitude and direc-tion across frequency space was obtained by plot-ting the cospectra of velocity and concentration:

u0c0 ¼ vfF

ZT0

Cucðf Þdt ð7Þ

where Cuc(f) is cospectral density at a frequency f,vf is cospectral resolution and F cospectral fre-quency range, in this case 2 or 5 Hz. Sediment£ux contributions from incident and infragravitywaves were separated at a frequency of 0.067 Hz.Sediment £uxes at a given station were eval-

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uated using the lowermost exposed OBS sensor inan array. Integrations over an instrument arraywere not attempted because: (a) sometimes onlyone or two sensors in an array were exposed and/or functioned properly, (b) under the (relativelyhigh) energy surf zone conditions sampled here,the bed was probably £at and phase lags betweenvelocity and sediment concentration were small(see below); consequently directional £ux rever-sals in the vertical were extremely rare, and (c)sediment concentrations increase towards thebed and the lowermost (exposed) OBS is consid-ered being more representative for the bulk sedi-ment transport.

5. Results

5.1. Observations

Fig. 3 illustrates net sediment £uxes recorded atbar crests (stations S3 at Staengehus and S2 atSkallingen) during a number of storm events. O¡-

shore wave conditions for these particular eventswere similar with signi¢cant wave heights peakingat 1.9 m (Staengehus) and 1.9, 1.8 and 2.3 m,respectively, for the three events at Skallingen.Local relative wave heights (Hs/h= Qs) exceeded0.60 at times of high wave energy and bar crestswere therefore located in the inner surf zone atsuch times. Even so, the net sediment £uxeswere directed o¡shore (negative values) at Staen-gehus while they were onshore (positive) for twoof the three events at Skallingen. As most sedi-ment transport models would predict o¡shore-di-rected sediment transports under such inner surfzone conditions, explanations of these contrastingobservations would seem to be required.In Fig. 4, the net £uxes are partitioned into

contributions from the undertow and waves atincident and infragravity frequencies. The twomajor transport mechanisms were the undertow,providing an o¡shore-directed sediment £ux, andthe incident waves which are responsible for on-shore £uxes. It is evident that at these positions,infragravity motions were of secondary impor-tance to the sediment £ux.

5.2. A sediment £ux index

When using backscatter sensors for measuringsediment concentrations in the ¢eld, uncertaintiesare introduced in such measurements and in esti-mates of suspended sediment £ux, because of thevariable elevations of the backscatter sensors rel-ative to the bed, which is caused by bed erosionand accretion. Fluxes are therefore di⁄cult tocompare spatially and temporally. In an attemptto reduce this problem, a normalized sediment£ux index, re£ecting the sediment transport direc-tion, Qd is formulated as:

Qd ¼Gqincfþ Gqmeanf

MGqincfMþ MGqmeanfMð8Þ

where Gqincf,Gqmeanf are the time-averaged magni-tudes of suspended sediment £ux due to oscilla-tory incident waves and to mean currents, respec-tively, and contributions from infragravity waveshave been ignored. Under the present conditions

Fig. 3. Net cross-shore suspended sediment £uxes (solid lines)recorded at (a) Staengehus (station S3) and (b) Skallingen(SK96; station S2). Positive £uxes are onshore-directed. Thedashed lines indicate the local relative wave height, Qs ( =Hs/h). Wave heights are saturated for QsW0.60.

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when rip currents were absent, the mean currentswere due to undertow, i.e. directed o¡shore (neg-ative). Oscillatory sediment £uxes at incident wavefrequencies, in contrast, were onshore-directed(positive) when waves were breaking (Figs. 3 and4). Hence, the net sediment £ux will be increas-ingly dominated by incident wave motions anddirected onshore when Qd attains positive values,and increasingly dominated by the mean compo-nent and directed o¡shore when Qd becomes neg-ative. When Qd = 0, the contributions from inci-dent waves and undertow are in balance and thepro¢le should approximate a local equilibrium(apart from perturbations introduced by infra-gravity waves, gravity and bedload).

5.3. Sediment £ux directions in the surf zone

In Fig. 5, net suspended sediment £uxes (in-cluding the contribution from infragravity oscilla-tions) measured at Staengehus and Skallingenhave been plotted as a function of the local rela-tive wave height, Hs/h, which was used by Os-borne and Greenwood (1992) and Ruessink et

al. (1998) to parameterize cross-shore sediment£ux. Each data point represents an instrumentalrecord, i.e. a 34 (or 45)-min time average. Theexperimental data are not well-constrained. AtSkallingen, there was a tendency towards largeonshore-directed or smaller o¡shore-directed sedi-ment £uxes, irrespective of the magnitude of Hs/h.At Staengehus the data appear to conform tosome extent to the expected pattern, i.e. smalltransport rates for small values of the relativewave height (Hs/h6V0.5), trending to o¡shore-directed transport with increasing incident wave

Fig. 6. The non-dimensional sediment £ux, Qd, as a functionof local relative wave height, Hs/h. Only the lowermost ex-posed backscatter sensor was used.

Fig. 5. Measured net sediment £uxes at the lowermost OBSsensor, as a function of local relative wave height, Hs/h.

Fig. 4. Partitioned suspended sediment £uxes due to mean£ows, incident and infragravity waves at (a) Staengehus (sta-tion S3) and (b) Skallingen (SK96; station S2). Positive£uxes are directed onshore.

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dissipation, but then reversing to almost zero netsediment £uxes for the large values of Hs/h, whichwere observed during storm peaks at the crest ofthe inner bar.Fig. 6 illustrates the sediment £ux index (Qd,

which ignores infragravity wave contributions)as a function of the relative wave height. Again,a correlation does not appear to exist and anytrend is di⁄cult to discern. For the present dataset, it must be concluded that Hs/h is not a suit-able parameterization/predictor of sediment £uxrates or directions under breaking waves.Instead it may be more informative to consider

the actual processes contributing to the net cross-shore sediment £ux. The £ux due to the incidentwaves must depend at least in part on the max-imum cross-correlation (p) between oscillatory ve-locity at incident wave frequencies and the sedi-ment concentration in the water column, i.e. thestrength of the phase coupling (Ja¡e et al., 1984).In the case of large positive correlations at smallphase lags, the transport by incident waves should

be large and in the direction of wave propagation.With increasing phase lags or negative correla-tions caused, for example, by the existence of bed-forms or increasing sensor elevation above thebed, the sediment £ux direction may be oppositeto the direction of the waves, or much reduced.For the present data set, maximum cross-correla-tions between cross-shore velocity and sedimentconcentration at incident wave frequencies werealmost consistently positive, except for a few casesunder non-breaking or weakly breaking waves.Furthermore, the time lags at maximum correla-tion were consistently small, usually within 1 s.Fig. 7 illustrates examples of cross-correlationsbetween high-pass ¢ltered orbital velocities andsediment concentrations at all three backscatterlevels for a range of computed values of thewave-induced skin-friction Shields parameter (aP).Phase lags at correlation peaks are small and,interestingly, they do not consistently increasewith sensor elevation above the bed. Furthermore,cross-correlations are not always largest for thelowermost sensor, which suggests a high degreeof vertical mixing of the water column withinthe surf zone.With a positive correlation maximum at a small

time/phase lag (e.g. Fig. 7) we would expect on-shore-directed sediment £uxes due to the incident

Fig. 8. The non-dimensional sediment transport index, Qd, asa function of D. A logarithmic ¢t through the data has a co-e⁄cient of determination of r2 = 0.884. There are 144 degreesof freedom (d.o.f.).

Fig. 7. Examples of cross-correlations of sediment concentra-tions at three OBS sensor elevations, and high-pass ¢lteredorbital velocity at (a) SK96; station S2, run 301_10, (b)STG98, station S2, run 73c, (c) STG98, station S3, run 73band (d) SK96, station S2, run 311_01. aP is the skin-frictionShields parameter due to waves. Note the progressively in-creasing bed shear stresses and the lack of consistent rela-tionships between cross-correlation and sensor elevation.

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waves and such £uxes will be enhanced by largeincident wave skewnesses (s ; Eq. 4) and orbitalvelocities (e.g. Bailard, 1981; Thornton et al.,1996; Gallagher et al., 1998). These three factorsshould therefore be important to the magnitudeof the onshore-directed sediment £ux. With re-spect to the o¡shore-directed £ux, this would beexpected to depend upon the strength of the meancurrent (u). Consequently, Fig. 8 illustrates Qd

plotted against a non-dimensional parameter Dwhich is expected to re£ect the tendency towardsonshore or o¡shore-directed sediment £ux. D isgiven by:

D ¼ pWsWurmsMuM

ð9Þ

Again, only the incident wave band contributionsare included in the calculations of p, s and urmsand only data with Hs/hv 0.40, i.e. breakingwaves, have been considered. A logarithmic ¢tthrough the data yields a coe⁄cient of determina-tion, r2 = 0.884, and the line of best ¢t is:

Qd ¼ 0:285 lnðDÞ þ 0:102 ð10Þ

This result is encouraging as most mechanisms ofimportance to the net £ux seem to be included inEq. 9 and D appears to be a suitable parameterfor determining the balance between incidentwave £uxes and £uxes due to the undertow.When DsV0.7, the incident waves dominatethe sediment £ux and the net £ux is consequentlydirected onshore; when D6V0.7, mean currentsdominate with a resulting o¡shore-directed net£ux.Despite the good ¢t, this formulation is pres-

ently not well-suited for predictive and/or model-ling purposes as incident wave skewness and u^ccross-correlation, in particular, are di⁄cult to de-termine a priori. Therefore, s, p and u were testedagainst a range of environmental properties, in-cluding: (a) the relative wave height (Hs/h) ; (b)the surf similarity parameter (I= Lb/k(Hb/L0),where Lb is nearshore slope at the breakpointand L0 is deepwater wavelength); (c) the normal-ized water depth (h/hb), where hb is water depth atthe breakpoint; (d) 6 ( =Hb/wsT, where ws is thesediment fall velocity) ; (e) radiation stress gra-

dients (dH2/dx) ; and (f) the Shields parameter(a= d/b(s31)gd50), where d is the bed shear stress,b(s31) is the relative sediment density, and d50 isthe mean sediment grain size (Aagaard andGreenwood, 1999).

5.4. Undertow velocity

Undertow velocity (u) should depend upon lo-cal cross-shore radiation stress gradients (whichdepend on H2) and scale inversely with localwater depth (e.g. Svendsen, 1984). However, localstress gradients are di⁄cult to determine fromsensors spaced some 20^40 m apart and estimatedradiation stress gradients had no predictive powerwith respect to the undertow. Instead, assumingQ=H/h= constant over (small) spatial increments,a slope dependency is expected, i.e. :

UO

vH2=vxh

¼ Q2vhvx

¼ Q2tanL ð11Þ

where L is local slope. Hence, undertow velocitiesare expected to be larger over steep beaches thanon gently sloping beaches (Longuet-Higgins,1983). Fig. 9 illustrates the functional relationshipbetween undertow velocity and (Q2s tan L). Datafrom stations S4 and S5 in the intertidal zone atSkallingen (SK96; Fig. 2) have been included toincrease the spread in the data. The nearshore

Fig. 9. Mean cross-shore current (undertow) velocity (u) plot-ted against the square of the local relative wave height multi-plied by the local slope. A linear ¢t yields r2 = 0.494 with 256d.o.f.

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slope was determined from the pro¢le segmentimmediately seaward of the instrument station.While there is a substantial amount of scatter inthe data, a linear ¢t yields a coe⁄cient of deter-mination, r2 = 0.494 which is statistically signi¢-cant at the 1% level. The line of best ¢t is:

U ¼ 39:29ðQ 2s tan L Þ30:028 ð12Þ

Scatter is expected to be introduced by (a) mea-surement inaccuracies with respect to the determi-nation of slope; these slopes were calculated frompro¢le surveys before and after storms; (b) lateralmixing of turbulent kinetic energy; at Staengehus,the maximum cross-shore (and longshore) currentvelocities were often observed over the landwardslope of the middle bar instead of at the bar crest(see also e.g. Greenwood and Sherman, 1986); (c)the assumption of spatially constant relative waveheights ; Qs did vary signi¢cantly between neigh-boring instrument stations, and (d) the assump-tion of a constant undertow velocity in the verti-cal and/or the assumption that the recordedvelocities were in fact mean undertow velocities.Current meters were typically mounted 0.20^0.30m above the bed which appears to be a reasonableelevation at which to obtain mean undertow ve-locities (Masselink and Black, 1995). However,even though the water column may have beenwell-mixed due to the wave breaking, some verti-cal strati¢cation of current velocities probably ex-isted.

5.5. Wave skewness

Incident wave skewness (s) would be expectedto depend on o¡shore wave steepness and somemeasure of distance relative to the breakpoint, aswave skewness tends to reach a peak at the break-point and decrease systematically onshore, at leastfor planar beaches (e.g. Thornton and Guza,1989). For barred beaches, Plant et al. (2001) re-cently obtained a relationship between wave skew-ness and the local relative wave height. For thepresent data, the best correlation for s was ob-tained with the product of the local relativewave height (Hs/h) and the local relative waterdepth, de¢ned as h/hb, with hb being water depth

at breaking. At Skallingen where the nearshoreslope seaward of the bars is very small, hb wasdetermined as the water depth at the toe of theoutermost bar. It is at this point that strong wavedissipation and deformation of the wave form be-gins during high-energy conditions, even thoughdepth-limited wave breaking did occur at timesseaward of the outer bar. At Staengehus, thebars are steep with deep troughs where incidentwaves reform. Therefore, hb was determined fromHs/0.35 with the wave height being estimatedfrom depth-corrected wave records in the troughsbetween bars. Hence, for stations on the inner bar(S6, S7), hb was estimated as Hs(S5)/0.35 and forstations on the second bar (S2, S3), hb was esti-mated as Hs(S1)/0.35. A linear regression throughall data (Fig. 10) yields a coe⁄cient of determina-tion r2 = 0.418. In all but two cases (not includedin the ¢gure), wave skewnesses were positive andthus directed onshore. Scatter in the data is ex-pected at least partly due to the uncertain deter-mination of the breakpoint position. Interestingly,the functional relationship shown in Fig. 10 didnot improve when o¡shore wave steepness wasincluded in the predictor.

5.6. u^c cross-correlation

The cross-correlation between £uid velocity andsediment concentration (p) is expected to dependat least in part upon bed con¢guration. When

Fig. 10. Incident wave skewness (s) as a function of the localratio between signi¢cant wave height and breaker depth.r2 = 0.418; 200 d.o.f. The line of best ¢t is s=1.332 (Hs/hb)+0.004.

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non-dimensional bed shear stresses are small(aP6V0.2^0.4; Nielsen, 1992), vortex ripplesgenerally occur at the seabed. Well-developed vor-tex ripples tend to result in relatively large cross-correlations between velocity and concentrationbut with large phase lags, up to 90‡ as sedimentis ejected from the bedforms at velocity reversals(e.g. Nakato et al., 1977; Osborne and Green-wood, 1993). For increasing bed shear stresses,ripples are washed out and the cross-correlationand phase coupling between u and c are expectedto degrade. Flat bed conditions are initiated foraPW0.7^1.0 (Wilson, 1989; Watanabe et al., 1991;Nielsen, 1992). With £at beds, the cross-correla-tion between velocity and sediment concentrationclose to the bed again becomes relatively large butwith small phase lags (Ribberink and Al-Salem,1992; Black and Vincent, 2001). Hence, a localminimum in u^c cross-correlation is expected at

moderate values of the Shields parameter. Suchincreasing cross-correlations/phase couplings withincreasing bed shear stresses (aP=0.6^2.0) are il-lustrated in Fig. 11 where examples of (demeaned)cross-shore velocity and sediment concentrationwere phase-averaged over 40 wave-cycle bins. Be-low the £at bed criterion (Fig. 11a), the patternof suspended sediment concentration displays asmall peak between wave crest and downwards£ow reversal and the maximum cross-correlation(p) between u and c is small. A phase coupling isnot evident. With increasing bed shear stresses,the patterns change to a primary peak at thewave crest and a secondary peak at £ow reversal(Fig. 11b). In this example, the computed bedshear stresses exceed the £at bed criterion butthe resuspension patterns suggest the presence ofsome remnant bedforms. For very large bed shearstresses (Fig. 11c,d), the suspended sediment con-centration becomes increasingly similar to the ve-locity trace and p increases signi¢cantly. In thesecases, the phase coupling between u and c is verystrong.Correlations between orbital velocity and sedi-

ment concentration are also generally consideredto depend upon the distance between a sensor andthe bed (e.g. Ribberink and Al-Salem, 1992; Os-borne and Greenwood, 1993; Black and Vincent,2001). Even though the present data suggest thatin the surf zone, this dependency may not bestraightforward, at least close to the bed (Fig.7), estimates of p were restricted to data fromOBS sensors positioned within approximately0.10 m from the bed. Bed elevation was deter-mined at low tide at Skallingen. During SK95,bed level changes were generally small (withinM 0.05 m over tidal cycles at station S2) and thesensors were adjusted at each low tide. DuringSK96, bed level changes were considerably largerand sensor adjustments were often impossible dueto high energy levels. However, at the bar crest(S2), accretion occurred during storms and thus atleast one backscatter sensor was within 0.10 mfrom the bed. At Staengehus, the bars eroded sig-ni¢cantly during storms and the optical sensorswere often well away from the bed. Approximatesensor elevations on the middle bar were deter-mined from the bed elevation sensors; only data

Fig. 11. Phase averages of cross-shore velocity and sedimentconcentration at the lower (solid), mid (short dashes) andupper (long dashes) OBS sensors for increasing values of thenon-dimensional bed shear stresses (the skin-friction Shieldsparameter due to waves) and u^c cross-correlations. (a)SK96, station S2, run 301_10, (b) STG98, station S2, run73c, (c) SK96, station S2, run 311_01 and (d) SK96, stationS2, run 310_10. Only one OBS sensor was exposed in thelast example.

MARGO 3088 7-6-02


points for which the lower sensor was estimatedas being less than 0.10 m from the bed have beenincluded in the present analysis.The skin-friction Shields parameter was com-

puted using the non-linear wave-current boundarylayer model proposed by Soulsby (1997):

amax ¼dmax

b ðs31Þgd50ð13Þ

The maximum bed shear stress is computed as:

dmax ¼ ½ðdm þ d0cos P Þ2 þ ðd 0sin P Þ21=2 ð14Þ

where P is the angle between the direction of waveincidence and the mean current (computed astan31(v/u) where demeaned and high-pass ¢ltered,and mean values of the cross-shore and longshorevelocity components (u,v) were used, respectively),and dP is the wave-induced bed shear stress due tograin roughness:

d0 ¼ 1=2b f wu2s ð15Þ

us was determined as 2(c2u+c2v)1=2 where c

2 is or-bital velocity variance, and fw is the wave frictionfactor:

f w ¼ exp�5:213ðks=AÞ0:19435:977

�ð16Þ

(Swart, 1974) and the bed roughness, ks, was setequal to the grain roughness ( = 2.5 d50). In Eq.16, A is the orbital diameter near the bed, deter-mined as A= (usTp/2Z), where Tp is peak spectralwave period. Further, in Eq. 14 the current-in-duced bed shear stress modi¢ed by the wave mo-tion is:

dm ¼ d c 1þ 1:2d0

d0 þ d c

� 3:2

� �ð17Þ

(Soulsby, 1997) and the mean current induced bedshear stress in the absence of waves is:

d c ¼ b

uUlnðz=z0Þ

� 2 ð18Þ

where U is the von Karman constant = 0.40 andz0 = ks/30 = d50/12.The data (Fig. 12) indicate that a signi¢cant

(at the 1% level) positive linear correlation(r2 = 0.324) existed between the Shields parameterand the u^c cross-correlation for amaxs 0.5 with aline of best ¢t of p=0.356amax30.130. Hence, cor-relation increased with increased £attening of thebed, which is what was expected. The relationshipis weak, however, and scatter is undoubtedly in-troduced by, for example, temporal (undetected)changes in grain size and lags in bedform adjust-ment to changes in bed shear stress (Davidson etal., 1993), as well as changing sensor elevations(within a V0.1-m vertical range).

5.7. A prediction of sediment £ux directions in thesurf zone

Consequently, substituting amax for p, Hs/hb for s,and (Q2s tan L) for u, a new parameter, y, is ob-tained:

y ¼ amaxWðHs=hbÞWurmsðQ 2

s Wtan L Þ ð19Þ

Regressing y against Qd yields the functional re-lationship:

Fig. 12. Correlation between high-pass ¢ltered oscillatory ve-locity and suspended sediment concentration (p) as a func-tion of the non-dimensional bed shear stress (amax) underbreaking waves in the surf zone. r2 = 0.324; 124 d.o.f. Onlymeasurements below z=0.1 m have been included.

MARGO 3088 7-6-02


Qd ¼ 0:026y30:752 ð20Þ

with a coe⁄cient of determination, r2 = 0.579(Fig. 13). When y exceeds approximately 30, thenet suspended sediment transport close to the bed(z6V0.1 m) tends to be directed landwards,while y6 30 results in a tendency for o¡shoresediment transport. There is signi¢cantly morescatter in this relationship than in Fig. 8 whichis probably to a large extent due to the di⁄cultieswith predicting p.

5.8. Sediment concentrations and net sediment£uxes in the surf zone

Qd (Eq. 20) predicts the tendency for onshoreor o¡shore sediment £ux, and the magnitude ofthat tendency. However, to obtain at least a semi-quantitative estimate of near-bed (z6V0.10 m)sediment £uxes, information is required about theconcentrations of sediment in the water column.Such concentrations should depend upon eleva-tion above the bed, bed con¢guration and bedshear stress (e.g. Nielsen, 1992; Black, 1994; Mas-selink and Pattiaratchi, 2000), as well as wavebreaker type (e.g. Kana, 1978; Beach and Stern-berg, 1996; Voulgaris and Collins, 2000).

Sediment mixing in the water column can beconsidered as either a di¡usive process, which isgenerally associated with £at beds, or a convectiveprocess which usually occurs when the bed isrippled. In both cases, the vertical distributionof sediment concentration can be formulated as:

Cz ¼ C0exp 3wszO s

� ð21Þ

(e.g. Nielsen, 1984) where Cz is sediment concen-tration at elevation z, C0 is a reference concentra-tion near the bed, ws is the sediment fall velocity,Os is an eddy di¡usion coe⁄cient and z is eleva-tion above the seabed. By using the mixing lengthconcept and assuming Os is constant in the verti-cal, i.e. ls = (dz/dln C) = (Os/ws), Eq. 21 can be re-written:

Cz ¼ C0exp 3zls

� ð22Þ

This general formulation has been found to workwell under a variety of ¢eld conditions and with£at as well as rippled beds (e.g. Black, 1994;Green and Black, 1999; Masselink and Pattia-ratchi, 2000).Based on ¢eld and laboratory studies, Nielsen

(1986) suggested that the reference concentrationcould be expressed by:

C0 ¼ 0:005a 03 ð23Þ

where aP is the skin-friction Shields parameter dueto waves ( = dP/(p(s31)gd50). Turning to the pre-diction of C0 and ls from the present data sets, themixing lengths are expected to depend on the pro-cesses causing sediment redistribution in the watercolumn. If sediment concentration under breakingwaves and with £at beds is mainly a result ofdi¡usion, we would expect the mixing length toscale with the bed shear stress, while in the case ofconvection, for example due to breaker-inducedturbulence, we would expect ls to scale with thesize and intensity of breaker vortices (Nadaokaet al., 1988; Ting, 2001). The characteristics ofnear-bed breaker vortices associated with various

Fig. 13. The non-dimensional sediment transport index, Qd,as a function of the environmental parameter, y. A linear ¢tyields r2 = 0.579; 144 d.o.f.

MARGO 3088 7-6-02


breaker types and factors determining their scaleare not well known. However, the local relativewave height would appear to be a reasonable ¢rstguess as plunging breakers and high breaking in-tensities occur for large values of the relative waveheight (e.g. Wright and Short, 1984; Beach andSternberg, 1996).Following Masselink and Pattiaratchi (2000),

time-averaged mixing lengths for individual in-strument runs were determined from the measure-ments of sediment concentration at three OBSlevels, using ls = dz/dln c and computing the lineof best ¢t from the three data points. Only caseswhen the bed level was recorded and stable be-tween two low tides, or when the bed positionwas known from the bed elevation sensors wereincluded. Even so, exact OBS sensor elevationsrelative to the bed must be viewed as crude esti-mates. There was no statistically signi¢cant rela-tionship between the mixing length scale and thebed shear stress (r2 = 0.094) but a relationship be-

tween ls and Hs/h was obtained (Fig. 14a) with aline of best ¢t:

ls ¼ 0:057expð2:889ðHs=hÞÞ ð24Þ

and r2 = 0.480. The data suggest that mixinglengths within the surf zone are on the order of0.1^1.0 m which agrees with results from earlier¢eld studies by Black and Rosenberg (1991), Ji-menez et al. (1997), Masselink and Pattiaratchi(2000) and Voulgaris and Collins (2000) but aresigni¢cantly larger than values obtained over £atbeds in the laboratory (e.g. Boers, 1999). The mix-ing length increased as the relative wave heightincreased from Hs/hW0.15 to Hs/hW0.65, cor-responding to a range from non-breaking con-ditions through spilling breakers and into theplunging breaker regime. Hence, the relationshipbetween ls and Hs/h could be due to an increasingdiameter of breaker-induced vortices near the bedas the relative wave height increases and/or largevertical velocities associated with plunging break-ers.However, Eq. 24 is dimensional and to non-

dimensionalize the relationship, ls was scaled bythe local water depth which also resulted in animproved correlation:

lsh¼ 0:012expð4:781ðHs=hÞÞ ð25Þ

and r2 = 0.583, Fig. 14b. The reason for the im-proved correlation may be that the diameter ofbreaker vortices is depth-limited, particularly inshallow water where the relative wave height ismaximum. There was no signi¢cant correlationbetween ls and the local value of the surf scalingparameter as was observed by Voulgaris and Col-lins (2000).Subsequently, C0 was computed from Eq. 22

using the obtained estimates of ls. In Fig. 15, C0

is plotted against the Shields parameter. The di-mensional form of C0 has been chosen, usingbs = 2650 kg/m3 and a pore space factor aP=0.6.In Fig. 15a, all available computed reference con-centrations have been plotted against aP in orderto compare the data with the original formulation(Eq. 23). While Eq. 23 does pass through thecluster of data points, there is a large amount of

Fig. 14. (a) The vertical mixing length scale, ls, plottedagainst the local relative wave height, Hs/h. r2 = 0.480;d.o.f. = 96. (b) The mixing length, scaled by the local waterdepth, as a function of the local relative wave height.r2 = 0.583; d.o.f. = 96.

MARGO 3088 7-6-02


scatter. The majority of the scatter may be due tomeasurement inaccuracies with respect to z and lsand some may be due to the existence of bed-forms and the resulting £ow acceleration at ripplecrests which will increase a and hence referenceconcentrations (e.g. Green and Black, 1999).In Fig. 15b, only data points obtained from the

surf zone (and with aPs 0.8, i.e. £at bed condi-tions) are included. Under conditions with break-ing waves and in the presence of strong currents,amax (Eq. 12) is probably a more appropriate mea-sure of the actually occurring bed shear stressesthan aP and Fig. 15b suggests that for high-energysurf zones, C0 = 0.0015 a

3max might be a better ap-

proximation than Eq. 23.Having found reasonable predictors for near-

bed sediment concentrations, these are combinedwith the sediment £ux index in order to obtain a¢rst approximation of net suspended sediment£uxes (Qs) in the near-bed layer (z6V0.1 m)under surf zone conditions across nearshore bars:

Qs ¼ ð0:026y30:752ÞU

0:0015b sa0a 3maxexp 3

z0:012expð4:781ðHs=hÞÞ

� ð26Þ

where the dimensional form of the reference con-centration has been used and Qs has the dimen-sion of kg/m2/s.

6. Discussion

The process-based formulation of the sedi-ment transport direction in the near-bed layer(z6 0.1 m), which has been proposed here (Fig.8), seems to capture the majority of the mecha-nisms which are responsible for cross-shore trans-port of suspended sediment due to incident wavesand undertows. The results indicate that the nettransport direction depends upon the maximumcross-correlation between orbital velocity and sedi-ment concentration (p), the incident wave skew-ness (s) and the mean current speed (u). The de-gree of scatter in Fig. 8 is relatively small giventhe wide range of possible measurement errors(e.g. instrument o¡set errors, errors due to vary-ing sensor elevation above the bed, temporalchanges in sediment grain size, etc.).Signi¢cantly more scatter was introduced when

Qd was instead correlated with a set of predictablehydrodynamic, textural and bathymetric proper-ties (Eqs. 19 and 20), even though correlationswere all statistically signi¢cant at the 1% level(Figs. 9, 10 and 12). As expected, the incidentwave skewness depended upon local relative waterdepth and wave height, the u^c cross-correlationdepended upon the non-dimensional bed shearstress probably through a relationship betweenthe latter and bed con¢guration, while the meancurrent velocity depended upon local relativewave height and bed gradient. However, factorsother than amax, Hs/hb and (Q2tan L) are clearlyimportant to p, a and u. Some of the scatter in thecorrelations may be due to the fact that fw, andamax were computed using the plane-bed (grain)roughness, ks = 2.5 d50. The calculated values ofamax for surf zone conditions ranged between 0.61and 2.12 and post-vortex ripples may have oc-curred occasionally, especially in the lower endof this range, increasing the bed roughness. Fur-thermore, large sediment concentrations whichare expected to increase the roughness (e.g. Glennand Grant, 1987) were not taken into account.Nevertheless, Eqs. 19 and 20 suggest that rela-

tively large water depths with moderate wavebreaking on gentle slopes, and large bed shearstresses should promote landward sediment trans-port due to incident waves. However, landward

Fig. 15. (a) The near-bed reference concentration (C0) plot-ted against the skin-friction Shields parameter due to waves(aP). The solid line represents C0 = 0.005 aP

3. (b) C0 plottedagainst amax and for surf zone conditions only. The solid linerepresents C0 = 0.005 a

3max and the dashed line is C0 = 0.0015

a3max.

MARGO 3088 7-6-02


transports can occur even with saturated wavebreaking (Figs. 3 and 4) if bed shear stresses aresu⁄ciently large and slopes su⁄ciently small. Onthe other hand, small water depths and intensewave breaking on steep slopes should promoteseaward transport. The former situation is ex-pected to occur typically some distance awayfrom the shoreline and/or at high tide/stormsurges during high wave energy events and en-hanced by strong longshore currents; the lattersituation will typically occur in the inner part ofthe surf zone.Surprisingly, no direct functional dependency

between transport direction and sediment grainsize and/or sediment fall velocity seemed to existin the present data set. Obviously, this might bebecause the spectrum of grain sizes was relativelynarrow and grain size e¡ects may have been over-shadowed by other mechanisms. However, thenon-dimensional bed shear stress is inversely de-pendent upon sediment grain size and addition-ally, steep slopes which enhance the undertow ve-locity generally occur for coarser grain sizes.Hence, within the surf zone of relatively coarse-grained beaches there should be a tendency fornegative values of Qd and a propensity for o¡-shore sediment transport while the oppositeshould be the case for relatively ¢ne grain sizeswhich are usually associated with gently slopingbeaches.This proposed parameterization would be capa-

ble of predicting bar formation/location as a func-tion of sediment transport convergences withinthe surf zone without resorting to mechanismssuch as standing infragravity waves. Bar positionwould be determined by a balance between thee¡ects of bed shear stress and water depth, gen-erally decreasing onshore (except for troughs be-tween bars), and the e¡ect of relative wave heightwhich is typically increasing in the onshore direc-tion. It is clear, however, that this balance can beperturbed by the velocity ¢eld set up by infragrav-ity waves, the e¡ects of which are not included inthe model. Consequently, the formulation is notexpected to be valid when infragravity waves playa predominant role in the suspension and trans-port of sediment, e.g. in very shallow water depthsclose to the shoreline.

The above concept could also provide an expla-nation for the frequently observed approach toequilibrium conditions during storms, or indeedthe occurrence of an ‘equilibrium pro¢le’. Oftenbeaches erode signi¢cantly at the beginning of astorm, or storm sequence (through o¡shore sedi-ment transport), while relatively limited changeoccurs later on (e.g. Lee et al., 1998). Accordingto the present model, the reason could be that assediment is eroded from the intertidal beach orfrom the bar crest and deposited on seaward slopes,the overall beach pro¢le is £attened and undertowvelocities should decrease. Subsequently, Qd (andQs) could increase and approach a balance whereQdW0.The formulation of the sediment transport in-

dex (Eqs. 19 and 20) is based on the assumptionthat cross-correlations between oscillatory veloc-ity and sediment concentration are constant in thenear-bed layer (z6 0.10 m) and that phase lagsare negligible. Surf zone data from these two ¢eldsites do suggest that under strongly breakingwaves, there is a high degree of vertical mixingin the water column. Phase lags between orbitalvelocity and sediment concentration were consis-tently found to be small and did not signi¢cantlyincrease with elevation relative to the bed, andcross-correlations did not exhibit any consistentdecrease with increasing elevation (Fig. 7).The model for the sediment concentration pro-

¢le, proposed by Nielsen (1984), Eq. 21, has beenapplied for surf zone conditions. The present datasuggest that mixing length scales are signi¢cantlylarger within the surf zone compared to locationsoutside the breakpoint, and the magnitudes are inaccordance with previous ¢ndings by Black andRosenberg (1991) and Masselink and Pattiaratchi(2000). Again, no direct dependency was foundbetween the mixing length and sediment fall ve-locity, mean grain size or local bed shear stress.Thus, there appears to be a real di¡erence in thesediment resuspension mechanisms over £at bedswithin and outside the surf zone; in the lattercase, sediment suspension is primarily accom-plished by turbulent di¡usion close to the bedwith small mixing length scales (e.g. FredsUeand Deigaard, 1992; Black and Vincent, 2001),while within high-energy surf zones, mixing length

MARGO 3088 7-6-02


scales are probably increased signi¢cantly by thegeneration of breaker-induced turbulent vorticesand possibly large vertical velocities just prior tobreaking.The expression for near-bed reference concen-

trations suggested by Nielsen (1984) seems towork reasonably well for high-energy surf zoneconditions. Even with the poor control on exactsensor elevation, the data points were relativelywell constrained by the expression (Eq. 23) anddisplayed the expected cubic relationship withthe non-dimensional bed shear stress. However,when waves coexist with strong currents, forexample within the surf zone, the wave-inducedbed shear stresses (aP) in isolation may not bean adequate representation of true bed shearstresses as the non-linear interaction betweenwaves and currents in the near-bed layer signi¢-cantly increases shear stress at the bed (e.g. Grantand Madsen, 1979). Accordingly, when using amax

instead of aP, the constant of proportionality inEq. 23 needs to be reduced by approximately afactor of three.Finally, the sediment transport index was com-

bined with the parameterization of the sedimentconcentration pro¢le under breaking waves into aformulation of suspended sediment transportrates in the near-bed layer (Eq. 26). There is am-ple scope for improvement of this model andadditional work is required to incorporate infra-gravity £uxes and their spatial and temporal var-iability. Furthermore, the model is restricted tothe near-bed layer and even though the majorityof suspended sediment transport probably doesoccur close to the bed, the high degree of verticalmixing observed here shows that signi¢cantamounts of sediment are suspended to large ele-vations above the seabed. However, a predictionof sediment transport at higher elevations wouldrequire a parameterization of p as a function ofelevation which would probably have to rely onprototype scale laboratory measurements as theexact determination of bed elevation under ¢eldconditions is extremely di⁄cult.In general, an improved understanding of p and

its dependency on factors other than a (e.g. bed-forms (active and relict) and large sediment con-centrations) are required. The poor prediction of

p (Fig. 12) is probably one of the main sources ofincreased scatter in Fig. 13 relative to Fig. 8.Improved predictions of incident wave skew-

nesses in barred surf zones as well as a parameter-ization of horizontal and vertical undertow struc-ture would also enhance the validity of the model.The latter would require a determination of hor-izontal and vertical mixing due to turbulent inci-dent wave bores. Finally, the prediction of ls (Eq.25) is not well-constrained and obviously factorsother than the relative wave height and waterdepth are of signi¢cant importance to the mixinglength scale in the surf zone. Investigation of im-portant additional mechanisms would in all like-lihood require detailed numerical modelling and/or large scale laboratory measurements underbreaking waves. Regardless of these reservations,however, the proposed model appears to providea reasonable ¢rst approximation to near-bed sus-pended sediment transport across nearshore barsin the surf zone.

7. Conclusions

In this paper, a relationship between sediment£ux directions in the near-bed layer and a limitednumber of hydro- and sediment dynamic param-eters was obtained. These parameters includedwave orbital velocity and skewness, the cross-cor-relation between orbital velocity and sedimentconcentration, and the undertow velocity. How-ever, these parameters are di⁄cult to predict andwere substituted with a number of more easilyobtainable hydrodynamic, sedimentary and bathy-metric parameters. While the degree of predictingskill degraded, as would have been expected, theobtained relationships were still signi¢cant at the1% level.The model predicts onshore-directed sediment

transports for large bed shear stresses in relativelydeep water occurring on gently sloping beaches.Such characteristics are associated with largewave orbital velocities and asymmetries, largebed shear stresses and relatively weak cross-shorecurrents. With increased breaking intensity inshallow water and for relatively steep nearshoreslopes, undertows increase and the sediment

MARGO 3088 7-6-02


transport becomes o¡shore-directed. The magni-tude of the sediment transport depends on sedi-ment concentrations in the water column; thesewere found to depend upon bed shear stress and(probably) the diameter of breaker-induced vorti-ces.

Acknowledgements

This study was supported by the Danish NaturalSciences Research Council through Grant no.9701836 and 11-0925. JUrgen Nielsen, Ulf Tho-mas, Rasmus Nielsen and Kalle Kronholm pro-vided invaluable field assistance. We would alsolike to thank the North Zealand Forest Districtfor giving us permission to work at Staengehus.Parts of this paper were written up while the firstauthor was a visiting academic at the Departmentof Earth Sciences, University of Waikato. We ap-preciate the comments made by the reviewers onan earlier version of this manuscript.

References

Aagaard, T., 2001. Modulation of surf zone processes on abarred beach due to changing water levels. J. Coast. Res. 17.

Aagaard, T., Greenwood, B., 1994. Suspended sediment trans-port and the role of infragravity waves in a barred surf zone.Mar. Geol. 118, 23^48.

Aagaard, T., Greenwood, B., 1999. Directionality of cross-shore sediment transport in the surf zone under high-energyconditions. Proc. Coastal Sediments ’99, ASCE, pp. 1003^1018.

Aagaard, T., Nielsen, J., Greenwood, B., 1998. Suspendedsediment transport and nearshore bar formation on a shal-low intermediate-state beach. Mar. Geol. 148, 203^225.

Aagaard, T., Greenwood, B., Nielsen, J., 2001. Bed levelchanges and megaripple migration on a barred beach.J. Coast. Res., SI 34.

Bailard, J.A., 1981. An energetics total load sediment trans-port model for a plane sloping beach. J. Geophys. Res. 86,10938^10954.

Beach, R.A., Sternberg, R.W., 1991. Infragravity driven sus-pended sediment transport in the swash, inner and outer surfzones. Proc. Coastal Sediments ’99, ASCE, pp. 114^128.

Beach, R.A., Sternberg, R.W., 1996. Suspended-sedimenttransport in the surf zone: Response to breaking waves.Cont. Shelf Res. 16, 1989^2003.

Birkemeier, W.A., Long, C.E., Hathaway, K.K., 1997. Delilah,

Duck94 and SandyDuck: Three nearshore ¢eld experiments.Proc. 25th Coast. Eng. Conf., ASCE, pp. 4052^4065.

Black, K., 1994. Suspended sediment load during an asymmet-ric wave cycle over a plane bed. Coast. Eng. 23, 95^114.

Black, K., Rosenberg, M.A., 1991. Suspended sediment loadat three timescales. Proc. Coastal Sediments ’91, ASCE,pp. 313^327.

Black, K.P., Vincent, C.E., 2001. High-resolution ¢eld mea-surements and numerical modelling of intra-wave sedimentsuspension on plane beds under shoaling waves. Coast. Eng.42, 173^197.

Boers, M., 1999. E¡ect of wave breaking and bed friction onsuspended sediment concentration. Proc. Coastal Sediments’99, ASCE, pp. 209^224.

Davidson, M.A., Russell, P.E., Huntley, D.A., Hardisty, J.,1993. Tidal asymmetry in suspended sand transport on amacrotidal intermediate beach. Mar. Geol. 110, 333^353.

Elgar, S., Gallagher, E.L., Guza, R.T., 2001. Nearshore sand-bar migration. J. Geophys. Res. 106, 11623^11627.

FredsUe, J., Deigaard, R., 1992. Mechanics of Coastal Sedi-ment Transport. World Scienti¢c, Singapore, 369 pp.

Gallagher, E.L., Elgar, S., Guza, R.T., 1998. Observations ofsand bar evolution on a natural beach. J. Geophys. Res.103, 3203^3215.

Glenn, S.M., Grant, W.D., 1987. A suspended sediment strat-i¢cation correction for combined wave and current £ows.J. Geophys. Res. 92, 8244^8264.

Grant, W.D., Madsen, O.S., 1979. Combined wave and cur-rent interaction with a rough bottom. J. Geophys. Res. 84,1797^1808.

Grasmeijer, B.T., van Rijn, L.C., 1999. Breaker bar formationand migration. Proc. 26th Coastal Engineering Conference,ASCE, pp. 2750^2758.

Grasmeijer, B.T., Chung, D.H., van Rijn, L.C., 1999. Depth-integrated sand transport in the surf zone. Proc. CoastalSediments ’99, ASCE, pp. 325^340.

Green, M.O., 1999. Test of sediment initial-motion theoriesusing irregular-wave ¢eld data. Sedimentology 46, 427^442.

Green, M.O., Black, K.P., 1999. Suspended-sediment referenceconcentration under waves: Field observations and criticalanalysis of two predictive models. Coast. Eng. 38, 115^141.

Greenwood, B., Davidson-Arnott, R.G.D., 1979. Sedimenta-tion and equilibrium in wave-formed bars: A review andcase study. Can. J. Earth Sci. 16, 312^332.

Greenwood, B., Sherman, D.J., 1986. Longshore current pro-¢les and lateral mixing across the surf zone of a barrednearshore. Coast. Eng. 10, 149^186.

Huntley, D.A., Hanes, D.M., 1987. Direct measurement ofsuspended sediment transport. Proc. Coastal Sediments’87, ASCE, pp. 723^737.

Ja¡e, B.E., Sternberg, R.W., Sallenger, A.H., 1984. The role ofsuspended sediment in shore-normal beach pro¢le changes.Proc. 19th Coast. Eng. Conf., ASCE, pp. 1983^1996.

Jimenez, J.A., Rivero, F.J., Sanchez-Arcilla, A., Gracia, V.,Rodriguez, A., 1997. Suspended sediment mixing in thesurf zone. Proc. 25th Coast. Eng. Conf., ASCE, pp. 4098^4110.

MARGO 3088 7-6-02


Kana, T.W., 1978. Surf zone measurements of suspended sedi-ment. Proc. 16th Coast. Eng. Conf., ASCE, pp. 1725^1743.

Komar, P.D., 1998. Beach Processes and Sedimentation, 2ndedn. Prentice-Hall, Englewood Cli¡s, NJ, 544 pp.

Larson, M., Kraus, N.C., 1989. SBEACH: Numerical modelfor simulating storm-induced beach change. CERC TR 89-9,256 pp.

Lee, G.H., Nicholls, R.J., Birkemeier, W.A., 1998. Storm-driv-en variability of the beach-nearshore pro¢le at Duck, NorthCarolina, USA, 1981^1991. Mar. Geol. 148, 163^177.

Longuet-Higgins, M.S., 1983. Wave set-up, percolation andundertow in the surf zone. Proc. R. Soc. London A390,283^291.

Masselink, G., Black, K.P., 1995. Magnitude and cross-shoredistribution of bed return £ow measured on natural beaches.Coast. Eng. 25, 165^190.

Masselink, G., Pattiaratchi, C., 2000. Tidal asymmetry in sedi-ment resuspension on a macrotidal beach in northwesternAustralia. Mar. Geol. 163, 257^274.

Miller, H.C., Smith, S.J., Hamilton, D.G., Resio, D.T., 1999.Cross-shore transport mechanisms during onshore bar mi-gration. Proc. Coastal Sediments ’99, ASCE, pp. 1065^1080.

Nadaoka, K., Ueno, S., Igarashi, T., 1988. Sediment suspen-sion due to large eddies in the surf zone. Proc. 22nd Coast.Eng. Conf., ASCE, pp. 1646^1660.

Nakato, T., Locher, F.A., Glover, J.R., Kennedy, J.F., 1977.Wave entrainment of sand from rippled beds. J. Waterw.Port Coast. Ocean Div. ASCE 103, 83^99.

Nielsen, P., 1984. Field measurements of time-averaged sus-pended sediment concentrations under waves. Coast. Eng.8, 51^72.

Nielsen, P., 1986. Suspended sediment concentrations underwaves. Coast. Eng. 10, 23^31.

Nielsen, P., 1992. Coastal Bottom Boundary Layers and Sedi-ment Transport. World Scienti¢c, Singapore, 324 pp.

Osborne, P.D., Greenwood, B., 1992. Frequency dependentcross-shore suspended sediment transport. 2. A barredshoreface. Mar. Geol. 106, 25^51.

Osborne, P.D., Greenwood, B., 1993. Sediment suspensionunder waves and currents: Time scales and vertical struc-ture. Sedimentology 40, 599^622.

Plant, N.G., Ruessink, B.G., Wijnber, K.M., 2001. Morpho-logic properties derived from a simple cross-shore sedimenttransport model. J. Geophys. Res. 106, 945^958.

Rakha, K.A., Deigaard, R., BrUker, I., 1997. A phase-resolv-ing cross-shore sediment transport model for beach pro¢leevolution. Coast. Eng. 31, 231^261.

Ribberink, J.S., Al-Salem, A.A., 1992. Time-dependent sedi-ment transport phenomena in oscillatory boundary-layer£ow under sheet £ow conditions. Delft Hydraulics DataReport H840.20, Part VI, Delft.

Ridd, P.V., 1992. A sediment level sensor for erosion andsiltation detection. Est. Coast. Shelf Sci. 35, 353^362.

Ruessink, B.G., Houwman, K.T., Hoekstra, P., 1998. The sys-tematic contribution of transporting mechanisms to thecross-shore sediment transport in water depths of 3 to 9 m.Mar. Geol. 152, 295^324.

Ruessink, B.G., Terwindt, J.H.J., 2000. The behaviour of near-shore bars on the time scale of years: A conceptual model.Mar. Geol. 163, 289^302.

Russell, P.E., 1993. Mechanisms for beach erosion duringstorms. Cont. Shelf Res. 13, 1243^1265.

Russell, P.E., Huntley, D.A., 1999. A cross-shore transport‘shape function’ for high energy beaches. J. Coast. Res.15, 198^205.

Sallenger, A.H., Holman, R.A., 1985. Wave energy saturationon a natural beach with variable slope. J. Geophys. Res. 90,11939^11944.

Schoonees, J.S., Theron, A.K., 1995. Evaluation of ten cross-shore sediment transport/morphological models. Coast. Eng.25, 1^41.

Shepard, F.P., 1950. Beach cycles in Southern California. U.S.Army Corps of Engineers, Beach Erosion Board, Techn.Memo 15, 31 pp.

Soulsby, R., 1997. Dynamics of Marine Sands. Telford, Lon-don, 249 pp.

Svendsen, I.A., 1984. Mass £ux and undertow in a surf zone.Coast. Eng. 8, 347^365.

Swart, D.H., 1974. O¡shore sediment transport and equilibri-um beach pro¢les. Delft Hydrol. Lab. Publ. 131, 247 pp.

Thornton, E.B., Guza, R.T., 1982. Energy saturation andphase speeds measured on a natural beach. J. Geophys.Res. 87, 9499^9508.

Thornton, E.B., Guza, R.T., 1989. Wind wave transformation.In: Seymour, R.J. (Ed.), Nearshore Sediment Transport.Plenum Press, New York, pp. 137^171.

Thornton, E.B., Humiston, R.T., Birkemeier, W.A., 1996. Bar/trough generation on a natural beach. J. Geophys. Res. 101,12097^12110.

Ting, F.C.K., 2001. Laboratory study of wave and turbulencevelocities in a broad-banded irregular wave surf zone. Coast.Eng. 43, 183^208.

Van Rijn, L.C., 1993. Principles of Sediment Transport inRivers, Estuaries and Coastal Seas. Aqua Publications, Am-sterdam.

Van Rijn, L.C., 1998. Principles of Coastal Morphology. AquaPublications, Amsterdam.

Van Rijn, L.C., Ruessink, B.G., Grasmeijer, B.T., 1999. Gen-eration and migration of nearshore bars under non- to mac-rotidal conditions. Proc. Coastal Sediments ’99, ASCE,pp. 463^478.

Voulgaris, G., Collins, M.B., 2000. Sediment resuspension onbeaches: Response to breaking waves. Mar. Geol. 167, 167^187.

Watanabe, A., Shimizu, T., Kondo, K., 1991. Field applicationof a numerical model of beach topography change. Proc.Coastal Sediments ’91, ASCE, pp. 1814^1828.

Wilson, K.C., 1989. Mobile bed friction at high shear stress.J. Hydraul. Eng. 115, 825^830.

Wright, L.D., Guza, R.T., Short, A.D., 1982. Dynamics of ahigh energy dissipative surf zone. Mar. Geol. 45, 41^62.

Wright, L.D., Short, A.D., 1984. Morphodynamic variabilityof beaches and surf zones: A synthesis. Mar. Geol. 56, 92^118.

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