DTIC ADA483327: Cross-Shore Distribution of Longshore Sediment Transport: Comparison Between Predictive Formulas and Field Measurements

22 Pages·0.34 MB·English

by  Defense Technical Information Center

CoastalEngineering44(2001)79–99
www.elsevier.com/locate/coastaleng
Cross-shore distribution of longshore sediment transport:
comparison between predictive formulas and field measurements
Atilla Bayrama, Magnus Larsona,*, Herman C. Millerb, Nicholas C. Krausc
aDepartmentofWaterResourcesEngineering,LundUniversity,Box118,S-22100,Lund,Sweden
bFieldResearchFacility,U.S.ArmyEngineerResearchandDevelopmentCenter,1261DuckRoad,Duck,NC,27949-4471,USA
cCoastalandHydraulicsLaboratory,U.S.ArmyEngineerResearchandDevelopmentCenter,3909HallsFerryRoad,
Vicksburg,MS,39180-6199,USA
Received29September2000;receivedinrevisedform12July2001;accepted18July2001
Abstract
Theskillofsixwell-knownformulasdevelopedforcalculatingthelongshoresedimenttransportratewasevaluatedinthe
present study. Formulas proposed by Bijker [Bijker, E.W., 1967. Some considerations about scales for coastal models with
movable bed. Delft Hydraulics Laboratory, Publication 50, Delft, The Netherlands; Journal of the Waterways, Harbors and
Coastal Engineering Division, 97 (4) (1971) 687.], Engelund–Hansen [Engelund, F., Hansen, E., 1967. A Monograph On
Sediment Transport in Alluvial Streams. Teknisk Forlag, Copenhagen, Denmark], Ackers–White [Journal of Hydraulics
Division,99(1)(1973)2041],Bailard–Inman[JournalofGeophysicalResearch,86(C3)(1981)2035],VanRijn[Journalof
HydraulicDivision,110(10)(1984)1431;110(11)(1984)1613;110(12)(1984)1733],andWatanabe[Watanabe,A.,1992.Total
rateanddistributionoflongshoresandtransport.Proceedingsofthe23rdCoastalEngineeringConference,ASCE,2528–2541]
were investigated because they are commonly employed in engineering studies to calculate the time-averaged net sediment
transportrateinthesurfzone.Thepredictivecapabilityofthesesixformulaswasexaminedbycomparisontodetailed,high-
quality data on hydrodynamics and sediment transport from Duck, NC, collected during the DUCK85, SUPERDUCK, and
SANDYDUCK field data collection projects. Measured hydrodynamics were employed as much as possible to reduce
uncertaintiesinthecalculations,andallformulaswereappliedwithstandardcoefficientvalueswithoutcalibrationtothedata
sets.Overall,theVanRijnformulawasfoundtoyieldthemostreliablepredictionsovertherangeofswellandstormconditions
coveredbythefielddataset.TheEngelund–Hansenformulaworkedreasonablywell,althoughwithlargescatterforthestorm
cases,whereastheBailard–Inmanformulasystematicallyoverestimatedtheswellcasesandunderestimatedthestormcases.The
formulasbyWatanabeandAckers–Whiteproducedsatisfactoryresultsformostcases,althoughtheformeroverestimatedthe
transportratesforswellcasesandthelatteryieldedconsiderablescatterforstormcases.Finally,theBijkerformulasystematically
overestimated the transport rates for all cases. It should be pointed out that the coefficient values in most of the employed
formulaswerebasedprimarilyondatafromthelaboratoryorfromtheriverenvironment.Thus,re-calibrationofthecoefficient
valuesbyreferencetofielddatafromthesurfzoneisexpectedtoimprovetheirpredictivecapability,althoughthelimitedamount
ofhigh-qualityfielddataavailableatpresentmakesitdifficulttoobtainvaluesthatwouldbeapplicabletoawiderangeofwave
andbeachconditions.D 2001ElsevierScienceB.V.Allrightsreserved.
Keywords:Longshoresedimenttransport;Predictiveformulas;Fieldmeasurements
* Correspondingauthor.Fax:[phone].
E-mailaddress:[email protected](M.Larson).
0378-3839/01/$-seefrontmatterD2001ElsevierScienceB.V.Allrightsreserved.
PII:S0378-3839(01)00023-0
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4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Cross-shore distribution of longshore sediment transport: comparison
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between predictive formulas and field measurements
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80 A.Bayrametal./CoastalEngineering44(2001)79–99
1. Introduction mulas are assessed, as well as their limitations, using
various statistical measures. Finally, the conclusions
During the past three decades, numerous formulas of the study are presented in Section 6.
and models for computing the sediment transport by
wavesandcurrentshavebeenproposed,rangingfrom
quasi-steady formulas based on the traction approach 2. Longshore sediment transport formulas
of Bijker, and the energetics approach of Bagnold, to
complex numerical models involving higher-order Longshore sand transport is typically greatest in
turbulence closure schemes that attempt to resolve thesurfzone,wherewavebreakingandwave-induced
the flow field at small scale. There are relatively few currents prevail, although a pronounced peak can be
high-quality field data sets on the cross-shore distri- found in the swash zone as well (Kraus et al., 1982).
bution of the longshore sediment transport rate avail- Typically the total (or gross) longshore sediment
abletoevaluateexistingpredictiveformulas.Krauset transport rate is computed with the CERC formula
al. (1989) and Rosati et al. (1990) measured the (SPM,1984)inengineeringapplications.However,as
longshore transport rate across the surf zone using ability to predict the surf zone hydrodynamics has
streamertraps(i.e.,DUCK85andSUPERDUCKfield improved,theneedforreliableformulasthatspatially
experiments). Miller (1999) measured the cross-shore better resolves the sediment transport rate has
distribution with optical backscatter sensors (OBS) increased, both concerning the cross-shore distribu-
combined with current measurements (i.e., SANDY- tion of the transport rate and the concentration dis-
DUCKfieldexperiment).Themeasurementsreported tribution through the water column.
by Miller (1999) covered a number of storms, thus In this investigation, the skill of six published
complementing the measurements by Kraus et al. formulas proposed for calculating the cross-shore
(1989) and Rosati et al. (1990) that were made in distribution of the longshore sediment transport rate
milder swell waves. was investigated. Transport rates were calculated for
Theobjectiveofthepresentstudyistoevaluatethe theutilizedcasesusingstandardcoefficientvalues(as
predictive capability of six well-known sediment given in the literature) without calibration. In the
transport formulas, adapted to calculate the cross- present comparison the formulas proposed by Bijker
shore distribution of the longshore sediment transport (1967, 1971), Engelund and Hansen (1967), Ackers
rate, based upontheabove-mentioned three fielddata and White (1973), Bailard and Inman (1981), Van
sets. We selected formulas that have gained world- Rijn (1984), and Watanabe (1992) (as they chrono-
wide acceptance in confidently predicting longshore logically appeared in the literature) were employed,
sedimenttransportrates.This,however,shouldnotbe representing the most common approaches for calcu-
interpretedasasignofdisagreementoralesseningof lating the time-averaged net sediment transport rate.
the importance of formulas not discussed here. Only The Bijker and Van Rijn formulas also calculate the
sand transport was investigated in this study, and suspended sediment concentration distribution
focus is on computing the time-averaged net long- through the water column, which allowed for addi-
shore transport rate. tional comparisons for these two formulas with some
Background to the investigated sediment transport of the field cases for which concentration measure-
formulas are given in Section 2 and their main ments were made. This will be discussed in a forth-
characteristics are summarized (the equations used coming paper (Larson et al., in preparation).
to calculate the transport rate are given in Appendix ThesixformulasaresummarizedinTable1,where
A). Next, in Section 3, the longshore sediment trans- the formulas, coefficient values, and wave and beach
port data sets are described. In Section 4 are shown conditions of the data originally used for verification
the results of the comparisons between the formulas oftheformulasarelisted.Furtherdetailsregardingthe
andthefielddataincludingawiderangeofwaveand equations are given in Appendix A. This is necessary
currentconditions.Anoveralldiscussionoftheresults because some variants of the formulas have appeared
fromthecomparisonsisprovidedinSection5,where in the literature. In the following, a short background
the strength and weaknesses of the investigated for- to the formulas is presented together with their main
Table1
Longshoresedimenttransportformulas(fornotationseeAppendixA)
Formula Longshoresediment Coefficients Verificationdata
transportformula
D(mm) tanb Exp.condition
(cid:2) (cid:3)
V p (cid:3)0:27ðs(cid:3)1Þd qg
Bijker qb;B ¼Ad50C ffigffiffiffiffiexp ls 50 A=1–5 0.23 0.07 H0=1.6m;
b;wc
(cid:2) (cid:4) (cid:5) (cid:3)
33h
q ¼1:83q I ln þI
s;B b;B 1 r 2 (non-breaking–breaking) T=12.0s; A
.
B
a
0:05Cs2 a=13(cid:1) yr
Engelund–Hansen qt;EH ¼V ðs(cid:3)1Þ2d50bq;w2cg5=2 – 0.19–0.93 – – amet
a
l.
(cid:2) (cid:3) /
Watanabe qt;W ¼A ðsb;wc(cid:3)qgsb;crÞV A=0.5–2 0.2–2.0 0.2–0.01 H0=0.02–2.4m; Coas
ta
(regular–irregular) T=1.0–18.0s; lE
n
a=15–45(cid:1) g
Ackers–White qt;AW ¼V 1(cid:3)1 pd35(cid:4)VV(cid:7)(cid:5)nCAdm;grðFC (cid:3)AÞm A,m,n,Cd,gr,FC 0.2–0.61 – h=0.18–7.17m ineering
4
(notmodified) (seeAppendixA) 4
VanRijn qb;VR ¼0:25cqsd50D(cid:3)(cid:7)0:3sffisffiffi0bffiqffi;ffiwffifficffiffi(cid:2)s0b;wcsb(cid:3);crsb;cr(cid:3)1:5 – 0.1–0.2 – H0=0.07–0.2m; (2001)79
T=1.0–2.0s; –
1Z h v c 99
q ¼c Vh dz¼c VhF
s;VR a h V c a a=90(cid:1)
a a
(cid:4) (cid:5)
e d
Bailard–Inman qt;BI ¼0:5qfwu30ðq (cid:3)qbÞgtanc 2v þd3v eb=0.1;es=0.02 0.175–0.6 0.034–0.138 H0=0.05–1.44m;
s
e
þ0:5qf u4 s ðd u(cid:7)Þ T=1.0–11.0s;
w 0ðq (cid:3)qÞgw v 3
s s
a=2.8–18.9(cid:1)
8
1
82 A.Bayrametal./CoastalEngineering44(2001)79–99
characteristics as well as references to the original tion of motion was included in the original formula-
publications. Also, Van De Graaff and Van Oveerem tion. The same coefficient values are used for
(1979) can be consulted for a comprehensive sum- monochromatic and random waves.
mary of some formulas. They compared three formu-
las for the net longshore sediment transport, namely 2.3. The Ackers and White formula
the formulas by Bijker, Engelund–Hansen, and
Ackers–White, although they focused on the gross Ackers and White (1973) developed a total load
rate and made comparisons for a number of selected sediment transport formula for coarse and fine sedi-
hypothetical cases. ment exposed to a unidirectional current. Coarse
sediment is assumed to be transported as bed load
2.1. The Bijker formula witharatetakentobeproportionaltotheshearstress,
whereas fine sediment is considered to travel in
Bijker’s(1967,1971)sedimenttransportformulais suspension supported by the turbulence. The turbu-
one of the earliest formulas developed for waves and lence intensity depends on the energy dissipation
current in combination. It is based on a transport generated by bottom friction, which makes the sus-
formula for rivers proposed by Kalinske–Frijlink pended transport rate related to the bed shear stress.
(Frijlink, 1952). Bijker distinguishes between bed The empirical coefficients in the Ackers–White for-
loadandsuspendedload,wherethebedloadtransport mula (hereafter, called AW formula) were calibrated
dependsonthetotalbottomshearstressbywavesand against a large data set covering laboratory and field
currents. The suspended load is obtained by integrat- cases (HR Wallingford 1990; reported in Soulsby,
ing the product of the concentration and velocity 1997). Van De Graaff and Van Overeem (1979)
profiles along the vertical, where the reference con- modifiedtheAWformulatoaccountforshearexerted
centration for the suspended sediment is expressed as by waves.
a function of the bed load transport. In its original
form,thebed-loadformuladoesnottakeintoaccount 2.4. The Bailard and Inman formula
a critical shear stress for incipient motion, implying
thatanybedshearstressandcurrentwillleadtoanet Bailard and Inman (1981) derived a formula for
sediment transport. The Bijker transport formula both the suspended and bed load transport based on
(hereafter, called the B formula) is, in principle, the energetics approach by Bagnold (1966). Bagnold
applicableforbothbreakingandnon-breakingwaves. assumed that the work done in transporting the sedi-
However, different empirical coefficient values are ment is a fixed portion of the total energy dissipated
needed in the formula. by the flow. The Bailard–Inman formula (hereafter,
called BI formula) has frequently been used by
2.2. The Engelund and Hansen formula engineersbecauseitiscomputationallyefficient,takes
into account bed load and suspended load, and the
Engelund and Hansen (1967) originally derived a flowassociatedwithwaves(includingwaveasymme-
formula to calculate the bedload transport over dunes try) and currents can be incorporated in a straightfor-
in a unidirectional current by considering an energy ward manner. A reference level for the velocity
balance for the transport. Later, this formula (here- employed in the formula (normally taken to be 5.0
after, called EH formula) was applied to calculate the cm above the bed) must be specified.
totalsedimenttransportunderwavesandcurrents,and
modifications were introduced to account for wave 2.5. The Van Rijn formula
stirring (Van De Graaff and Van Overeem, 1979).
However,theirtheoryhaslimitationswhenappliedto Van Rijn (1984) proposed a comprehensive theory
graded sediments containing large amount of fine forthesedimenttransportrateinriversbyconsidering
fractions, causing predicted transport rates to be both fundamental physics and empirical observations
smaller than the actual transport rates. Similar to the andresults. The formulations were extended toestua-
Bijker formula, no threshold conditions for the initia- ries as summarized by Van Rijn (1993) (hereafter,
A.Bayrametal./CoastalEngineering44(2001)79–99 83
calledVRformula).Bedloadandsuspendedloadare specific location in the surf zone during a certain
calculated separately, and the approach of Bagnold time was collected using streamer traps oriented so
(1966) is adopted for computing the bed load. Sus- that the traps opposed the direction of the longshore
pended load is determined by integrating the product current. The traps, each consisting of a vertical
of the vertical concentration and velocity profiles, array of polyester sieve cloth streamers suspended
where the concentration profile is calculated in three on a rack, were deployed across the surf zone. The
layers. Different exponential or power functions are polyester cloth allowed water to pass through but
employed in these layers with empirical expressions retained grains with diameter greater than the 0.105
that depend on the mixing characteristics in each mm mesh, which encompasses sand in the fine
layer. grain size region and greater. From knowledge of
the trap mouth area, the trap efficiency, and the
2.6. The Watanabe formula measurement duration, the local transport rate was
derived. The trapping efficiency has been exten-
Watanabe (1992) proposed a formula for the total sively investigated through laboratory experiments
load (bed load and suspended load) based on the (Rosati and Kraus, 1988) allowing for confident
power model concept. The volume of sediments set estimates of the local longshore sediment transport
in motion per unit area is proportional to the com- rate.
bined shear stress of waves and currents, if the Wave height and period were measured using the
critical value for incipient motion is exceeded, and photopole method described by Ebersole and Hughes
this volume is transported with the mean flow (1987). This method involved filming the water
velocity. This formula has been widely used in Japan surface elevation at the poles placed at approxi-
for the prediction of, for example, beach evolution mately 6-m intervals across the surf zone utilizing
around coastal structures and sand deposition in as many as eight 16-mm synchronized cameras. The
harbors and navigation channels. The Watanabe for- bottom profile along the photopole line was surveyed
mula (hereafter, called W formula) and its coefficient each day. Fig. 1 shows surveyed bottom topography
values have been calibrated and verified for a variety along the measurement transect on September 6,
of laboratory and field data sets during the last 1985. The root-mean-square (rms) wave height
decade (e.g. Watanabe, 1987; Watanabe et al., (H ) at the most offshore pole was in the range
rms
1991). However, it has not yet been established of 0.4–0.5 m, and the peak spectral period (T ) was
p
whether the value of the non-dimensional coefficient in the range of 9–12 s (see Table 2). Long-crested
in the formula (A) is a constant or it depends on the waves of cnoidal form arriving from the southern
wave and sediment conditions. Different values are quadrant prevailed during the experiment, producing
employed for laboratory and field conditions, a longshore current moving to the north with a
whereas the same value is typically used for mono- magnitude of 0.1–0.3 m/s.
chromatic and random waves.
3.2. SUPERDUCK surf zone sand transport experi-
ment
3. Longshore sediment transport data sets
Patterned after the DUCK85 experiment, the
3.1. DUCK85 surf zone sand transport experiment SUPERDUCK surf zone sand transport experiment
was conducted during September and October 1986
The DUCK85 surf zone sand transport experi- (Rosati et al., 1990). However, at SUPERDUCK a
ment was performed at the U.S. Army Corps of temporal sampling method to determine transport
Engineers’ Field Research Facility at Duck, NC in rates was emphasized in which traps were inter-
September, 1985. Kraus et al. (1989) measured the changed from 3 to 15 times at the same locations.
cross-shore distribution of the longshore sediment Fewer runs are available where the cross-shore dis-
transport rate using streamer traps. Eight runs were tribution was measured (two runs were employed
made where the amount of sediment transported at a here; see Table 2).
84 A.Bayrametal./CoastalEngineering44(2001)79–99
Fig.1.BottomprofilesurveyedalongthemeasurementtransectonSeptember6,1985(DUCK85experiment).
Waves and currents were measured in the same on September 19, 1986. In contrast to the DUCK85
manner as for DUCK85. The wave conditions during experiment, barred profiles occurred several times
the experiment were characterized as long-crested during the SUPERDUCK experiment, although the
swell (T in the range 6–13 s) with a majority of two runs presented here involved shelf-type profiles.
p
the waves breaking as plunging breakers. The wave
height(H )atthemostseawardpolevariedbetween 3.3. SANDYDUCK surf zone sand transport experi-
rms
0.3 and 1.6 m during the experiment. A steady off- ment
shorewind(6–7m/s)wastypicallypresentduringthe
measurements. The mean longshore current speeds The SANDYDUCK experiment was conducted in
measured were in the range of 0.1–0.7 m/s. During thesamelocationastheDUCK85andSUPERDUCK
the experiment, the seabed elevation at each of the experiments (Miller, 1998). SANDYDUCK included
photopoles was surveyed once a day and Fig. 2 several major storms, complementing the measure-
shows, as an example, the surveyed bottom profile ments made during DUCK85 and SUPERDUCK.
Table2
Beachand wavecharacteristicsfor runs selectedfromthe DUCK85,SUPERDUCK, and SANDYDUCK experimentsfor comparisonwith
sedimenttransportformulas
Date Profiletype H (m) T (s) D (m) V (m/s)
rms p ref mean
Sept.5,1985,09.57 Shelf 0.50 11.4 2.14 0.11
Sept.5,1985,10.57 Shelf 0.46 11.2 1.80 0.17
Sept.5,1985,13.52 Shelf 0.54 10.9 2.19 0.17
Sept.5,1985,15.28 Shelf 0.46 11.1 1.94 0.22
Sept.6,1985,09.16 Shelf 0.48 12.8 1.40 0.30
Sept.6,1985,10.18 Shelf 0.36 13.1 2.14 0.29
Sept.6,1985,13.03 Shelf 0.42 10.1 2.43 0.22
Sept.6,1985,14.00 Shelf 0.36 11.2 2.34 0.18
Sept.16,1986,11.16 Shelf 0.60 10.1 2.20 0.20
Sept.19,1986,10.16 Shelf 0.59 10.1 2.66 0.17
March31,1997 Bar 1.36 8.0 6.70 0.49
April1,1997 Bar 2.92 8.0 6.82 1.10
October20,1997 Bar 2.27 12.8 6.44 0.53
February04,1998 Bar 3.18 12.8 8.59 0.60
February05,1998 Bar 2.94 12.8 6.83 0.45
H =root-mean-squarewaveheightatthemostoffshoremeasurementpoint;T =peakspectralperiod;D =waterdepthatthemostoffshore
rms p ref
measurementpoint;V =meanlongshorecurrentvelocityinthesurfzone.
mean
A.Bayrametal./CoastalEngineering44(2001)79–99 85
Fig.2.BottomprofilesurveyedalongthemeasurementtransectonSeptember19,1986(SUPERDUCKexperiment).
Sediment transport measurements were made using tration was measured at several points through the
theSensorInsertionSystem(SIS),whichisadiverless vertical as well as at a number of cross-shore loca-
instrument deployment and retrieval system that can tions. Simultaneously, the velocity was recorded and
operateinseaswithindividualwaveheightsupto5.6 the local transport rate was derived from the product
m (Miller, 1999). An advantage of the SIS is that it of the concentration and velocity.
allowsdirectmeasurementofwave,sedimentconcen- Longshore bars were typically present during
tration, and velocity together with the bottom profile SANDYDUCK, making it possible to assess the
duringastorm.TheSISisatrack-mountedcranewith effects of these formations on the transport rate dis-
the instrumentation placed on the boom. A standard tribution.Asanexample,thebottomprofilemeasured
SIS consists of OBS to measure sediment concentra- during the storm on October 20, 1997, is shown in
tion, an electromagnetic current meter for longshore Fig.3.ThebeachatDuckiscomposedofsandwitha
and cross-shore velocities, and pressure gauge for median grain size (d ) of about 0.4 mm at the
50
waves and water levels. The wave conditions and shoreline dropping off at a high rate to 0.18 mm in
meanlongshorecurrentvelocitiesforfivestormcases theoffshore.Intheregionwhered =0.18mm(most
50
employed in this investigation are described in Table ofthetypicalsurfzonewidth),sedimentsamplinghas
2.DuringtheSANDYDUCK experimenttheconcen- yielded d =0.15 mm (diameter corresponding 35%
35
Fig.3.BottomprofilesurveyedalongthemeasurementtransectonOctober20,1997(SANDYDUCKexperiment).
86 A.Bayrametal./CoastalEngineering44(2001)79–99
being finer)and d =0.24 mm (diametercorrespond- performed. A Shields curve was employed to deter-
90
ing 90% being finer) as typical values (Birkemeier et minethecriterionfortheinitiationofmotionbasedon
al., 1985). h, which was included in the formulas that have this
feature.
The roughnessheight was estimatedin the follow-
4. Evaluation of the formulas ing manner:
Measuredhydrodynamicswereemployedasmuch (cid:9) Flat bed: r is set equal to 2.5d , where d is
50 50
aspossibleintheformulastoreduce theuncertainties the median grain size (Nielsen, 1992)
inthetransportcalculations.Thermswaveheightand (cid:9) Rippled bed: r is calculated from the ripple
peak spectral wave period was used as the character- height and length and the Shields parameter
istic input parameters to quantify the random wave according to Nielsen (1992)
field.Valuesatintermediatelocationswherenomeas- (cid:9) Sheet flow: r is calculated from the Shields
urements were made were obtained by linear interpo- parameter and d according to Van Rijn
90
lation(notethatthisisthecauseforthediscontinuities (1984), where d is the grain size that 10%
90
in the derivative of the calculated transport rate dis- of the sediment exceeds by weight.
tributions). It was assumed that the incident wave
angle was small, implying that the angle between the The wave friction factor (f ) was computed based
w
waves and the longshore current was approximately on r using the formula proposed by Swart (1976),
90(cid:1). In the VR formula the undertow velocity is which is based on an implicit relationship given by
needed if the resultant shear stress is calculated (i.e., Jonsson (1966), assuming rough turbulent flow,
the shear stress resulting from the cross-shore and
longshorecurrentscombined).Noundertowmeasure-
(cid:4) r (cid:5)0:194 r
ments were available and the model of Dally and lnðf Þ¼(cid:3)5:98þ5:2 for: <0:63
w
a a
Brown(1995)wasemployedtocalculatethisvelocity. b b
r
The influence of the shear stress from the undertow f ¼0:3 for: (cid:10)0:63
w
a
wastypicallysmallcomparedtothatofthelongshore b
currentandwaves.Inafewcasesextrapolationofthe ð1Þ
currentfromthemostshorewardorseawardmeasure-
ment point was needed. On the shoreward side the where a is the amplitude of the horizontal near-bed
b
current was assumed to decrease linearly to become water particle excursion. For the purpose of compar-
zero at the shoreline, whereas at the seaward end the ing the predictive capabilities of the formulas, coef-
current was taken to be proportional to the ratio of ficient values proposed by the developers and
breaking waves (i.e., assuming that most of the coworkers were employed without any particular
current was wave-generated in this region). tuning of the coefficients. Predicted transport rates
The roughness height (r), which determines the withtheformulaswereconvertedtomassfluxperunit
friction factors for waves and current, is a decisive width before comparison with the measurements.
parameter that may markedly influence the sediment
transport rate, especially the bed load transport. Here, 4.1. Comparisons with DUCK85 data
the calculation of the roughness height was divided
into three different cases depending on the bottom Although simulations were carried out for all runs
conditions, namely flat bed, rippled bed, and sheet listed in Table 2, only four of the runs were selected
flow. The division between these cases was made for detailed discussion here. However, the overall
based on the Shields parameter (h), where h<0.05 conclusions given are based on the results from all
impliedflatbed,0.05<h<1.0rippledbed,andh>1.0 simulations. Fig. 4 shows predicted cross-shore dis-
sheet flow (Van Rijn, 1993). An iterative approach tributions of the longshore sediment transport rate
was needed because the bottom conditions are not with the different formulas for the experimental run
known a priori when the roughness calculation is at 0957 on September 5, 1985 (denoted 859050957
A.Bayrametal./CoastalEngineering44(2001)79–99 87
Fig.4.Comparisonbetweencalculatedandmeasuredcross-shoredistributionoflongshoresedimenttransportrateforRun859050957fromthe
DUCK85experiment.
from year/month/day/time, in accordance with Kraus gradedsedimentslargesuspensionmodifiestheveloc-
et al., 1989). It is noted that the AW, EH, and VR itydistributionsothattheassumptionsunderlyingthe
formulasyieldgoodpredictionswithinthesameorder formula are not satisfied (Engelund and Hansen,
of magnitude as the measured data, at least in the 1967). Another reason for the discrepancy might be
inner part of the surf zone. Contrarily, the B, BI, and the relatively strong influence of the predicted rough-
W formulas give significantly higher transport rates ness on the transport rate that the EH formula dis-
than the measurements, especially B and W. Some plays. Run 859051528 (see Fig. 5) indicated a
overestimation is expected for the B and BI formulas bimodal distribution with a large peak in the outer
becausetheydonottakeintoaccountthethresholdof surf zone (at around 145 m) and a small peak in the
sediment motion in their original formulations, inner surf zone (at around 125 m). In general, the
although this simplification would not account for formulasfailtocorrectlypredictthisshape,especially
the large deviations found for the B formula. Bijker the shoreward peak. This peak is probably a function
(1971) pointed out that his formula tended to over- of additional breaking and current generation close to
estimate the transport rate using the recommended the shoreline. Because no current measurements were
value on the main coefficient. available here, extrapolation was employed, implying
Figs. 5 and6 show calculated and measuredtrans- that some portion of the discrepancy is probably
port rates for the experimental runs 859051528 and causedbytheuncertaintyintheinputdataratherthan
859060916, respectively. All formulas except B and the formulas themselves.
W predicted longshore transport rates at the correct DuringRun859060916themostseawardtrapwas
order of magnitude, although the EH formula some- located outside the surf zone and a relatively small
what underpredicted the transport rate. Bearing in amountofsandwascollectedinit(Fig.6).Thus,there
mind that the sediment has a d of approximately is clear evidence that the longshore transport rate
50
0.18 mm at the site, the discrepancy between the EH dropped off steeply seaward of the break point.
formula and the measured rates might be due to Predictions by the AW, BI, EH, and VR formulas
limitations in the derivation of the formula. For fine- were in satisfactory agreement with the measured