This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright Author's personal copy ContinentalShelfResearch52(2013)190–202 ContentslistsavailableatSciVerseScienceDirect Continental Shelf Research journal homepage: www.elsevier.com/locate/csr Research papers Wave evolution across the Louisiana shelf Anita Engelstada,n, Tim Janssenb, T.H.C. Herbersc, Gerbrant van Vledderd, Steve Elgare, Britt Raubenheimere, Lincoln Trainorf, Ana Garcia-Garciag aDepartmentofGeosciences,SanFranciscoStateUniversity,SanFrancisco,CA94132,USA bTheissResearch,LaJolla,CA92037,USA cDepartmentofOceanography,NavalPostgraduateSchool,Monterey,CA93943,USA dEnvironmentalFluidMechanicsSection,CivilEngineeringandGeosciences,DelftUniversityofTechnology,2600GA,Delft,TheNetherlands eWoodsHoleOceanographicInstitution,WoodsHole,MA02543,USA fRoyalAustralianNavy,Australia gDepartmentofEarthandPlanetarySciences,UniversityofCaliforniaSantaCruz,SantaCruz,CA95064,USA a r t i c l e i n f o a b s t r a c t Articlehistory: Observationsandthird-generationwavemodelhindcastsofoceansurfacegravitywavespropagating Received3June2012 acrosstheLouisianashelfshowthattheeffectsofthemudenvironmentonwaveevolutionarecomplex Receivedinrevisedform andepisodic.Whereaslow-frequencywaves(0.04–0.20Hz)showaconsistentdecaysimilartoearlier 14September2012 studies,thepresenceofmudalsoappearstosuppressthedevelopmentofshortwaves(0.20–0.25Hz) Accepted16October2012 under fetch-limited growth conditions. Significant suppression of wave development under wind- Availableonline27October2012 forced conditions is found to occur almost exclusively during easterly winds when satellite images Keywords: show the Atchafalaya mud plume extends into the study area. These results suggest that episodic Wave–mudinteraction sedimentsuspensioneventswithhighmudconcentrationsintheupperwatercolumncanaffectthe Fetch-limtedwavegrowth evolutionofwindwaves. Wavedamping &2012ElsevierLtd.Allrightsreserved. Louisianashelf Atchafalayamudplume 1. Introduction etal.,2011),andthatgenerationofhigh-frequencywavesbywind duringfetch-limitedconditionscanbesuppressed(Trainor,2009). The propagation and transformation of ocean surface waves in Such observations suggest that new processes should be consid- coastal areas is affected by many processes, including refraction, eredinadditiontodirectwave–seafloorinteraction. dissipation,andwindforcing,andisimportantfornearshorecircula- Theobjectivesofthepresentworkaretoimproveunderstanding tion, mixing, and transport processes. The presence of extensive of how mud affects the nearshore wave energy balance for both muddyareasontheshelfandinthenearshoreisknowntostrongly longerswellwavesandshort,wind-drivenseas,andtheimplications affectcoastalwavetransformation.However,thephysicalprocesses forcoastalwavemodeling.Here,recentobservationsofwaveevolu- involved in the interaction between waves and mud, and the tion across the inner Louisiana shelf, collected over two months quantitative effects on the nearshore wave energy balance, are not during spring 2008 are presented. The experimental area is in the fullyunderstood. vicinityoftheAtchafalayaoutflow(Fig.1a),andischaracterizedby Idealized models have been derived based on a discrete two- extensivemuddepositsontheseafloorandhighlyvariablewaveand layerdescriptionofthewatercolumn,wheresurfacewavesdrive wind conditions (Section 2). To identify the effects of mud on the internal waves on the density interface (lutocline) between the waveenergybalance,the observationsarecomparedwithhindcast nearlyinviscidwaterandadissipative,muddybottomlayer(Gade, resultsfromathird-generationwavemodel(Section3),andsatellite 1958;DalrympleandLiu,1978;Ng,2000;Winterwerpetal.,2007; observations of sediment plumes are used to investigate causes of MacPherson,1980;PiedraCueva,1993;MeiandLiu,1987)through model-datadiscrepanciesduringwind-forcedconditions(Section4). directinteractionofthewave-inducednear-bedfluidmotionswith the mud. However, field observations show that short waves, whichdonotinteractstronglywiththeseafloor,alsoloseenergy 2. Fieldobservations while traversing muddy areas (Sheremet and Stone, 2003; Sheremet et al., 2005; Elgar and Raubenheimer, 2008; Sheremet 2.1. Fieldsite nCorrespondingauthor.Tel.:þ14152828690. WaveevolutionontheLouisianashelfiscomplexandshaped E-mailaddress:[email protected](A.Engelstad). by the semi-enclosed geometry of the Gulf of Mexico, which is 0278-4343/$-seefrontmatter&2012ElsevierLtd.Allrightsreserved. http://dx.doi.org/10.1016/j.csr.2012.10.005 Author's personal copy A.Engelstadetal./ContinentalShelfResearch52(2013)190–202 191 progradation of the eastern Chenier Plain (Fig. 1a) along a coast wheremostoftheshorelineisretreating(WellsandKemp,1981; Robertsetal.,1989;Drautetal.,2005a,b). 2.2. Instrumentation Instruments(Fig.1b)deployedontheinnershelffromFebruary 8toMarch29,2008includedtwodirectionalwavebuoyssampling continuously at 1.28Hz, six bottom-mounted acoustic Doppler velocimeters (ADV) equipped with a built-in pressure gauge (sampling 68-minute bursts at 2Hz every four hours), and five stand-alone bottom-mounted pressure recorders sampling con- tinuously at 2Hz (Fig. 1b). An acoustic Doppler current profiler (ADP)wasmountedoneachoftheADVbottomframesasaback- up instrument, sampling 34min wave bursts at 1Hz every hour. The instruments were arranged in two cross-shore arrays (here- afterreferredtoasthewesternandcentraltransects,Fig.1b)and analongshorearray(easterntransect;seealsoTable1,andTrainor, 2009; Engelstad, 2011). The western and central instrument transectsweredeployedinwaterdepthsrangingfrom13to5m, in a region with shore-parallel isobaths (Fig. 1b) on a fairly flat [bottomslopeO(1:1000)]shelf.Theeasterninstrumentarraywas locatedapproximately25kmoffthecoastandextendedontothe TrinityShoalinwaterdepths from 11to5.5m.Bottom-mounted instruments were recovered on March 2, 2008 (to check instru- ment operation, replace batteries, and retrieve the data), and redeployed on March 5, 2008. Time series lengths for all instru- ments (apart from the ADPs) were processed to fit the ADVs sampling length (68min duration time series every four hours). During the first deployment period, pressure–velocity data from theADVatstationpv4producednoisydataandwerereplacedby datacollectedbythecolocatedADP. The nearshore instrument array (Fig. 1b) consisted of 10 Fig.1. (a)StudyareaislocatedwestoftheAtchafalaya–VermillionBaysystemin bottom-mounted ADV-pressure sensor pairs along a cross-shore theGulfofMexico.(b)Bathymetry(blackcurvesareisobaths,unitsm)andsensor transect between 5- and 2-m water depths, deployed from locations.Bluedotsaretheinnershelfstationswheredw-stationsareDatawell February 14 to April 17, 2008. Time series were collected in DirectionalWaveriderbuoys,thepvareNortekVectorADV-pressuresensors,and pa are pressure sensors. The nearshore array of SONTEK Triton ADV-pressure 51-minuteburstsat2Hzevery2h.Thenearshorearrayconnected sensors(referencedinthetextasn1,n2,y.,n16),isindicatedwithredsquares. to the western inner shelf array so that the combined dataset Thegreentriangleshowsthelocationofthemeteorologicalbuoy.(Forinterpreta- includesa13km-long,instrumentedcross-shoretransectfrom13- tionofthereferencestocolorinthisfigurelegend,thereaderisreferredtothe to2-mwaterdepth.Windspeedanddirection(Fig.2aandb)were webversionofthisarticle.) measured with a meteorological buoy located along the western transect (Fig. 1b). Box core samples, taken in February 2008, decoupled from the Atlantic Ocean, and the presence of a identified a soft mud layer of less than 5cm at each site at the relatively wide, shallow shelf. Meteorological forcing usually is time of sampling (Trainor, 2009; Garcia-Garcia et al., in prepara- weak from May to September, except for the passage of an tion). Although no instrument burial was observed, given the occasional Hurricane in late summer-early fall. From October to highlydynamicsedimenttransportinthearea(710cmbedlevel April,coldfrontspassthroughtheareaevery3–7days,resulting changeswereobservedatthenearshorearray),itispossiblethat inlocallygeneratedwindseaswithawiderangeofwaveheights some changes in the surface mud layer thickness and rheology and directions, and associated wind-induced sea level variations couldhaveoccurredoverthecourseoftheexperiment. and coastal circulation patterns (Roberts et al., 1989; Moeller Topreventerrorsduetothedepth-attenuationofwave-induced etal.,1993).Althoughthesecoldfrontscandifferinintensityand pressure andvelocitysignals, andforconsistencyacrossdifferent duration, they typically cause a clockwise rotation of the wind instruments, a cut-off frequency of 0.25Hz was applied to all from a southerly direction during the pre-frontal stage to a observations. The data were subdivided into low- (0.04–0.20Hz) northerly direction during the post-frontal stage. High wind and high- (0.20–0.25Hz) frequency bands. Wave heights were speedsandrelativelylongerfetches(southerlywindsareapproxi- derivedfromthewavespectrumbetween0.04Hzand0.25Hz. mately onshore, Fig. 1) during the pre-frontal phase often gen- eratethemostenergeticwavefields. 2.3. Waveconditions SedimentdischargefromtheAtchafalayaRiveriscarriedalong the coast in the primarily westward-directed Atchafalaya mud A wide range of wind and wave conditions were observed stream(WellsandKemp,1981).Sedimentdepositionextendsto associatedwiththepassingofseveralcoldfrontsthroughthearea about92.551W(Drautetal.,2005a,b)andisrestrictedtoapproxi- (Fig. 2). The observed wave fields were dominated by locally mately shoreward of the 10m isobath (Allison et al., 2000). The generatedwindseaswithperiodsrangingfrom4to8s(Fig.2c) presenceofmudontheLouisianashelfisknowntodampenwave andmoderatewaveheights(Fig.2d),rarelyexceeding2m. energynearthecoast(SheremetandStone,2003;Sheremetetal., Duringfetch-limitedconditions(windcomingfromnortherly 2005;Kinekeetal.,2006;ElgarandRaubenheimer,2008;Trainor, directions), observed wave heights at similar depths vary 2009; Sheremet et al., 2011), and has been linked to the between the western and the eastern transect by as much as Author's personal copy 192 A.Engelstadetal./ContinentalShelfResearch52(2013)190–202 Table1 Station information for sensors: dw are Datawell Waverider buoys, pv are shelf pressure-velocity sensors, pa are pressure recorders; the n representcolocatedpressureandvelocitysensorsinthenearshore.Heightsabovetheseafloorofthebottom-mountedinstrumentswere1.35mfor theADPs,1.5mforthepressure–velocitysensors,and0.7mforthepressurerecorders.ThenearshorepressuresensorsandADVswerelocated 0.6mand0.9mabovethebottom,respectively. Stationname Latitude(Deg.North) Longitude(Deg.West) Depth(MSL)(m) Notes Westerntransect,shelf dw1 29.44418 92.63243 13.3 Availableonlyuntil03/05/2008 pv2 29.47670 92.62452 11.3 pa3 29.50370 92.60323 9.6 pv4 29.52315 92.59897 8.3 ADPusedfor1stleg pa6 29.55330 92.59190 4.6 Misplacedbyfisherboat,butdepthstillok Stationname Westerntransect,nearshore n16 29.55618 92.56444 4.0 n15 29.55764 92.5640 3.9 n14 29.55896 92.56389 3.7 n13 29.56041 92.56358 3.6 n12 29.5617 92.56331 3.4 n11 29.56311 92.56314 3.2 n9 29.56446 92.56289 2.8 n8 29.5660 92.56245 2.5 n7 29.56851 92.56195 2.2 n6 29.56999 92.56165 2.0 n5 29.57142 92.56120 1.9 n4 29.57273 92.56110 1.7 n3 29.57413 92.56084 1.4 n2 29.57543 92.56051 1.3 Stationname Centraltransect pv7 29.42407 92.49975 10.9 pa8 29.45290 92.49433 9.9 pv9 29.49110 92.47482 8.3 Stationname Easterntransect dw12 29.32995 92.48897 10.9 pv13 29.32675 92.43167 8.8 pa14 29.30833 92.38973 7.6 pa15 29.30785 92.31747 6.8 pv16 29.29388 92.26530 5.5 60%, with wave heights largest in the east during northwesterly dominated conditions on March 16–17, when strong winds are winds and larger in the west during northeasterly winds. For fromthenortheast(shadedinyellowinFigs.2bandc).Duringthe instance,onFebruary16,March9–10,and March16–17,during March16–17event(shadedinyellowinFig.3),waveheightson periodswithstrongnortheasterlywinds(theseeventsareshaded the eastern transect are fairly homogeneous (no along-array inyellowinFigs.2aandb),waveheightsonthewesterntransect variations), whereas wave heights along the western transect arelargest(comparethewaveheightsshadedinyellowin11.3m vary considerably, suggesting that local variations in the wave depth in Fig. 3a with those in 10.9m depth in Fig. 3b and c). field on the Louisiana shelf are considerably different during Alternatively,onFebruary27andMarch8,duringwindsfromthe fetch-limited generation events than during depth-controlled northwest (shaded in gray in Fig. 2a and b), waves are largest swellevents. alongtheeasterntransect(comparewaveheightsshadedingray The bathymetry surrounding the western transect is nearly in 11.3m depth in Fig. 3a with those in 10.9m depth in Fig. 3b alongshore uniform. Therefore, the observed decrease in wave and c). These differences may be caused by large variations in height for waves entering the region from southerly directions effectivefetchassociatedwiththeproximityofthecoastlinejust (compareFebruary29,March18–19,andMarch26inFig.3aand north of the western and central transects, and the extreme b with those dates in Fig. 2b) suggests that wave energy is lost shallow depths northeast of the eastern transect. In any case, duringonshorepropagation(furtheranalyzedbelow).Thelossin it suggeststhat locally generatedwaves, and fetch-limitedwave waveenergycouldbecausedbybottomfriction,wavebreaking, growthconditions,oftenareimportantinthisarea. or the interaction between waves and the seafloor mud layer in Spatial variations in wave height also areobserved on March thisarea(SheremetandStone,2003;Sheremetetal.2005;Elgar 18–19(Fig.3,shadedinblue)whenwindsarefromthesouthand and Raubenheimer, 2008; Trainor, 2009; Sheremet et al., 2011). wave periods are relatively long (Fig. 2, shaded in blue). The It is known that dissipation can be enhanced in muddy regions decrease in wave height during this period of longer-period through wave–mud interaction (Gade, 1958; Dalrymple and Liu, (swell-like)wavesisespeciallystrongonthe(alongshore)eastern 1978;Ng,2000;SheremetandStone,2003;Sheremetetal.,2005; transect in water depths between 10.9m and 5.5m (shaded in Elgar and Raubenheimer, 2008; Trainor, 2009; Sheremet et al., blue in Fig. 3c) and depths between 3.9m and 1.7m on the 2011),butitisdifficulttoseparatetheeffectsofseafloorrheology westerntransect(shadedinblueinFig.3a).Thespatialvariations from other processes affecting the wave evolution, in particular of longer-period wave heights differ from those for wind-sea because little is known about the mutual interaction between Author's personal copy A.Engelstadetal./ContinentalShelfResearch52(2013)190–202 193 Fig.2. (a)Windspeedand(b)winddirection(blackcurves)andmeanwavedirection(blue)atstationpv2in11.3mwaterdepthversustime.Directionsaredefinedas wherethewavesandwindarefrom.(c)Peakperiodsonthewesterntransectin11.3m(pv2,red)and1.7m(n4,black)waterdepth.(d)Significantwaveheightin11.3m (pv2,red)and1.7m(n4,black)waterdepth.Theblackdashedlinein(c)at6sandin(d)at1mareforreference.ThedatagapbetweenMarch2andMarch5isduring instrumentmaintenance.Shadedareasrefertoeventsdiscussedinthetextandindicateperiodswithlargespatialwavevariabilityandstrong(49m/s)windsfromthe northeast(yellow,0odiro801)andnorthwest(gray,300odiro3601),aswellasaperiodoflargeswell(blue).(Forinterpretationofthereferencestocolorinthisfigure legend,thereaderisreferredtothewebversionofthisarticle.) waves,currents,andmud,andthecorrespondingeffectsonwave stations(Fig.4).However,forfetch-limitedconditions(northerly dampingacrosstheshelf. winds), the model tends to overestimate wave heights (Fig. 5b), whereasduringonshorewavepropagation(southerlywinds),the agreementisconsiderablybetter(Fig.5a). 3. Analysis The overestimation of wave heights during fetch-limited con- ditionsismostnoticeableatthemoreseawardsensors(h4¼8m, Toisolatechangesinthewavefieldassociatedwiththepresence Figs. 4a and b, e.g. February 26 and March 23). Comparison of ofthemudontheseafloor,theobservedwaveevolutioniscompared observed with modeled spectra during fetch-limited conditions with hindcasts performed with a third-generation wave model (Fig.6)showsthatwaveenergyinputabovethepeakfrequencyis (SWAN,Booijetal.,1999).Thewavemodel(SWAN)wasappliedin greatlyover-estimatedinthemodel,whichresultsintheobserved non-stationary mode (see Appendix A for details) using observed overestimationofwaveheightsattheseawardstations.Itappears winds,waterlevels,currents,andwaveconditions(boundaries),and thatduringslantingfetchandfetch-limitedconditions,windwave run with a standard JONSWAP bottom friction term (Hasselmann generationishinderedorsuppressed(Fig.6)whencomparedwith etal.,1973)withoutadditionalphysicstoaccountfortheinteraction the model-predicted evolution (see also Trainor, 2009). This withamudlayer.Theobjectivewastoapplythemodeltorepresent model-data discrepancy could be caused either by enhanced wave evolution over an equivalent sandy shelf with the same dissipation on the inner shelf (not accounted for in the model), geometry, and for the same conditions as present during the or by suppression of wind-wave generation in this area, both experiment, so that systematic effects of the mud on the wave associated with the presence of mud on the seafloor and in the evolutioncanbedistinguishedfromtheinteractionofwaveswitha water column.Someofthesedifferencesalsocouldbecaused by sandybottom(bottomfriction),othersourcesofdissipationsuchas modelerrorsintherepresentationofshallowwater,fetch-limited wave breaking and white-capping, and processes such as wind wavegrowthconditions(Ardhuinetal.,2007). generation,nonlinearity,refractionandshoaling. During other times, for instance on March 10 and March 26, observed and modeled wave heights agree at the most seaward 3.1. Waveheights stations (h4¼8m, Fig. 4a and b), but wave heights are system- aticallyover-predictedneartheshore(ho¼4m,Fig.4candd).The The model hindcasts are in fairly good agreement with the same trend is observed during relatively weak wind forcing, observed wave height variability during the experiment for all suggesting that observed bottom-induced dissipation is stronger Author's personal copy 194 A.Engelstadetal./ContinentalShelfResearch52(2013)190–202 Fig.3. Significantwaveheightversustimeacross(a)thewesterntransectin11.3-(pv2,redcurve),8.3-(pv4,black),3.9-(n15,blue),and1.7-m(n4,green)waterdepths, (b)thecentraltransectin10.9-(pv7,red)and8.3-m(pv9,black)waterdepths,and(c)theeasterntransectin10.9-(dw12,red)and5.5-m(pv16,black)waterdepths. Thedashedblacklinesat1mheightareforreference.DatagapsforshelfstationsbetweenMarch2andMarch5areduetoinstrumentmaintenance.Shadedareasreferto eventsdiscussedinthetextandindicateperiodswithlargespatialwavevariabilityandstrong(49m/s)windsfromthenortheast(yellow,0odiro801)andnorthwest (gray,300odiro3601),aswellasaperiodoflargeswell(blue).(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversion ofthisarticle.) Fig.4. Observed(redcurveswithdots)andmodeled(blackcurveswithtriangles)significantwaveheightalongthewesterntransectversustimein(a)11.3,(b)8.3,(c)3.9, and(d)1.7mdepth.Thedatagaps(panelsa,andb)betweenMarch2andMarch5areduringinstrumentmaintenance.(Forinterpretationofthereferencestocolorinthis figurelegend,thereaderisreferredtothewebversionofthisarticle.) Author's personal copy A.Engelstadetal./ContinentalShelfResearch52(2013)190–202 195 Fig.5. Modeledversusobservedsignificantwaveheightforallstationsonthewesternandcentraltransectsfor(a)onshorewinds(1301–2501truenorth)and(b)offshore winds(3101–701).(Cross-shoreisrotated101clockwisefromtruenorth).Thedashedblacklinesindicateperfectagreement.Theslopeofthebest-fitlineis0.94for(a)and 1.18for(b),r2¼0.94for(a)andr2¼0.71for(b),andtherootmeansquareerroris0.11mfor(a)and0.19mfor(b). Fig.6. Observed(redcurveswithcircles)andmodeled(blackcurveswithtriangles)variancedensities(toppanels)andwavedirections(bottompanels)versusfrequency forstationsin(aande)1.7,(bandf)3.9,(candg)8.3,and(dandh)11.3mdepthintheafternoonofFebruary26.Wavedirectionisdefinedaswherethewavescome from.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.) than predicted by the model, consistent with observations from wave angle of incidence at each frequency (measured positive previousstudies(SheremetandStone,2003;Sheremetetal.2005; counterclockwise from shore-normal, which is set at 101 from ElgarandRaubenheimer,2008;Trainor,2009,Sheremetetal.2011). trueNorth).Theenergyfluxgradient,dF=dx,isestimatedthrough finite differencing over adjacent stations (for both the model hindcastsandtheobservations).Theuseoftheone-dimensional 3.2. Localenergybalance energy balance (Eq. (1)) is reasonable because the bathymetry nearthewesternandcentraltransectisalongshoreuniformand Differences between observed and modeled wave height values are the result of the accumulation of differences in the gradientsinthealongshoredirectioncanbeneglected. Overall, the hindcast predictions of the magnitude and the energy balance along the propagation path of waves over the inner shelf, and are not readily related to local differences in spectral distribution of the flux gradients agree reasonably well withtheobservations(compareFig.7awithFig.7bandcompare theenergybalance.Toidentifysuchlocaldifferences,considerthe one-dimensionalenergybalanceassumingstationaryconditions Fig. 7d with Fig. 7e), both offshore (h48m) and nearshore (ho4m).Theeventscharacterizedbylarge,negativefluxgradi- dF ¼S ð1Þ ents are associated with strong dissipation (mostly in the low- dx frequency band (0.04–0.20Hz)), and occur during times of high where S represents the sum of the source terms for dissipation, waveenergy. nonlinearity, and generation, and the cross-shore wave energy Differences between model and observations are greatest at flux,F,isdefinedas higherfrequencies(Z0.2Hz),especiallyat the seawardstations (compareFig.7awithb),wherethemodeldoesnotreproducethe F¼rgEc cosy ð2Þ g observeddissipation.Incontrastwiththeobservationsthatshow Here, r and g are (constant) density and gravitational accelera- either no growth (e.g. February 18, March 24 in Fig. 7a) or tion,Eisthevariancedensity,c isgroupspeed,andyisthemean dissipation (around March 17 in Fig. 7a), the model predicts a g Author's personal copy 196 A.Engelstadetal./ContinentalShelfResearch52(2013)190–202 a h=11.3 m (pv2) – 8.3m (pv4) dF/dx - observations )] s 2 m ( J/ [ b dF/dx-model )] s 2 m ( J/ [[ c Variance density - observations z] H / 2 mm [ d h=3.9 m(n15)–2.5m(n8) dF/dx - observations ]) s 2 m ( J/ [ e dF/dx-model )] s 2 m ( J/ [ f Variance density - observations z] H / 2 m [ Fig.7. Contours(colorscalesontheright)of(aandd)observedenergyfluxgradients,(bande)modeled(SWAN)energyfluxgradients,and(candf)observedenergy densityasafunctionoffrequencyandtime.a–carebetween11.3and8.9mdepthandd–farebetween3.9and2.5mdepth.Positivefluxgradientsindicategeneration, negativefluxgradientsindicatedissipation.Notethedifferentscalesof(a)and(b)versus(d)and(e). numberofwavegrowthevents(positiveenergyfluxgradientsin consistent with previous findings of wave–mud damping in the Fig.7b)wherewindinputdominatesoverdissipation. region(SheremetandStone,2003;Sheremetetal.,2005;Kineke Closertoshore,wheredissipationratesusuallyarelarger(and et al., 2006; Elgar and Raubenheimer, 2008; Trainor, 2009; thus dominate over possible local generation), the model-data Sheremet et al., 2011). However, the observed spectral distribu- agreement in the spectral distribution is generally better (com- tion of the dissipation associated with wave–bottom interaction pareFig.7dwithe). agreesfairlywellwiththemodeleddissipation(JONSWAPbottom The differences between the modeled and observed energy friction),suggestingthatthespectralsignatureofdissipation(and fluxgradientssuggestthatdissipationinthelow-frequencyband itsdependencyonrelativedepth)issimilar. (mostly owing to wave–bottom interaction) at this field site is However,animportantdifferencebetweenmodelanddatais somewhat higher than on an equivalent sandy shelf (see e.g. theobserveddissipation(orlackofgrowth)athigherfrequencies February 17, March 1 and March 17, compare Fig. 7a with b), (Z0.2Hz) at the deeper instrument sites whereas the model Author's personal copy A.Engelstadetal./ContinentalShelfResearch52(2013)190–202 197 Fig.8. Modeledversusobservedintegratedgrowthratesbetween11.3m(pv2)and8.3m(pv4).Integrationlimitsare(a)0.04–0.20Hzand(b)0.20–0.25Hz.Positive (negative)valuesindicategrowth(dissipation)rates.Notedifferentverticalandhorizontalscalesin(a)versus(b).Redcirclesindicatetimeswithwindcomingfrom between301and1301truenorthandblacktrianglesareforallotherdirections.Cross-shoreisrotatedabout101clockwisefromtruenorth.Onlyeventsforwhich HsZ0.5matpv2areshown.Thedashedblacklinesindicateperfectagreement.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredto thewebversionofthisarticle.) Fig.9. Observed(redcircles)andmodeled(blacktriangles)growthrates(right-handaxis)andwind(graycurve)andcurrent(greendashedcurve)directions(left-hand axis)versustime.OnlyeventsforwhichHsZ0.5matpv2areshown.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtotheweb versionofthisarticle.) predictsgeneration(Figs. 7a and b).To investigatethese model- In contrast, the observed enhanced (relative to the model) data differences for a range of wind and wave conditions, but dissipation at low frequencies (o0.2Hz) shows no correlation withoutthedependencyontheenergyinthewavefield,consider with wind direction (Fig. 8a, data left of the dashed line in the thenormalizedfluxgradient,orgrowthrate,k,definedas lower left quadrant), consistent with a bottom-induced damping effect that does not depend strongly on either the wind or wave dF1 direction. Thus, the model-data comparisons suggest that the k¼ ð3Þ dxF processes affectingthe dissipationin the low-frequency band are different than those in the high-frequency band. Moreover, where F¼rgEc is averaged between adjacent stations over whereas the observed enhanced damping of longer waves could g whichthefluxgradientisestimated. be consistent with existing theory based on direct interaction of Theeventsduringwhichmodeledgrowthratesofthehigher- surfacewaveswiththelutocline(thedensityinterface),itremains frequency components greatly exceed observed growth rates unclearwhythedifferencesbetweenobservedandmodeledwave (Fig. 8b, data in upper left quadrant) occur almost exclusively growthshowastrongdependencyonwinddirection. duringeasterlywinds,suggestingthatthemodel-datadiscrepan- Partofthesystematicdifferencesforfetch-limitedgrowthduring cies are related either to the specific fetch geometry or to other easterly winds may be owing to model shortcomings in the repre- physical parameters associated with the wind direction (and sentation of slanting fetch wave growth conditions (Ardhuin et al., changes therein). There appear two exceptions (Fig. 8b, black 2007). However, these observations do not show the frequency- trianglesintheupperleftquadrant),duringwhichtimethewind dependent shift in wave directions that is characteristic of slanting was not from the east, but dissipation is strong (model over- fetch wave growth conditions (Ardhuin et al., 2007). Moreover, predicts wave growth). However, note that during these times duringfetch-limitedconditionswithwindsfromthenorthwestand (seeMarch11inFig.9),althoughthewindhasturned,thecurrent north, the modelpredictions are generallyingood agreement with isstillfromtheeast(discussedmoreinSection4.2). the observations(February 18and March19in Fig. 9). It ismostly Author's personal copy 198 A.Engelstadetal./ContinentalShelfResearch52(2013)190–202 duringeasterlywindsthatlargedifferencesinthegrowthratesare (Fig. 9). The model-data comparisons suggest that the observed seen(dissipationinstead ofgrowth,March16–17inFig. 9),and as dependencyonwinddirectionsmostlikelyisassociatedwiththe soonasthewindturnstowest(throughsouth)themodelpredictions wave–muddynamics(andchangestherein),andnottheresultof agreewellwiththeobservations(March19inFig.9). modelshortcomingsunderfetch-limitedconditions. Another source of modeling errors of wave growth could be theinteractionwithlongerwaves(swell).However,duringmany of the cases where there are large differences in growth rates 4. Discussion between model and observations (February 16, March 10 and March 17 in Fig. 9), low-frequency energy levels were low 4.1. Wave–mudinteraction (Fig. 7c). In contrast, during other times when low-frequency energy levels are elevated (March 7 and March 20 in Fig. 9), Despite its importance, the characteristics and physical observed and modeled wave growth are in good agreement mechanisms of the interaction between surface waves and a Fig.10. Estimateoftotalsuspended-matterconcentrations(fromModis250imagery)on(a)March15,(b)March16,and(c)February28.Allimageswererecordedaround 17:00o’clockGMT.Highconcentrationsarered,lowconcentrationsareblue(colorscaleonright).Grayshadingisland.Instrumentlocationsareshownwithblackcircles (shelfstations)andredsquares(shorewardstations).(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthis article.)