Cliff retreat and sea bed morphology under monochromatic wave forcing: Experimental study

To link to this article : DOI: 10.1016/j.crte.2011.06.003

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Eprints ID: 10167

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Caplain, Bastien and Astruc, Dominique and Regard, Vincent and Moulin,

Frédéric Cliff retreat and sea bed morphology under monochromatic wave

forcing: Experimental study. (2011) Comptes Rendus Geoscience, vol. 343 (n°

7). pp. 471-477. ISSN 1631-0713

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Stratigraphy,

sedimentology

Cliff

retreat

and

sea

bed

morphology

under

monochromatic

wave

forcing:

Experimental

study

Recul

de

falaise

et

morphologie

du

fond

sableux

sous

un

forc

¸age

de

houle

monochromatique

:

e´tude

expe´rimentale

Bastien

Caplain

a,

*

,b

_,

_Dominique

_Astruc

a,b

_,

_Vincent

_Regard

c,d,e

_,

_Fre´de´ric

_Y.

_Moulin

a,b

a_{INPT,UPS,IMFT,Universite´ deToulouse,alle´eCamille-Soula,31400Toulouse,France} b_{CNRS,IMFT,31400Toulouse,France}

c_{UPS(OMP),GET,Universite´ deToulouse,14,avenueEdouard-Belin,31400Toulouse,France} d_{CNRS,GET,31400Toulouse,France}

e_{IRD,GET,31400Toulouse,France}

Keywords:

Clifferosion Seabedprofile Experimentalmodelling

Motscle´s:

E´rosiondefalaise Profildufond

Mode´lisationexpe´rimentale

Waveflumeexperimentshavebeenperformedtoinvestigateasandycliffrecessionunder monochromaticwaveforcing.WevariedthewaveclimatethroughthewaveenergyfluxF

andthesurfsimilarityparameterj.Thevariousprocessesoftheclifferosioncycleare depicted.Theseabedevolutionmostlydependsonthesurfsimilarityparameterj.Steep planar(j>0.7),gentleplanar(0.5<j<0.7)andbared(j<0.5)profilesareobserved.We observeddifferentbardynamics,includingsteadyandunsteadyself-sustainedoscillating states.Thenweanalyzetheroleoftheerodedmaterialonthecliffrecessionrate.Weshow thatthecliffrecessionrateincreaseswiththewaveenergyflux.Moreover,foragivenwave energyflux,itislargerforagentleplanarprofilethanforabaredprofile.Howeveritissimilar forbothabaredprofileandasteepplanarprofile.Thecliffrecessionrateisnotamonotonic functionofthecliffheightasthetypeofbottomprofileinfluencesthewaveenergyatthecliff.

RE´ SUME´

Desexpe´riencesencanala` houleonte´te´ re´alise´espoure´tudierlare´cessiond’unefalaisede sablesousunforc¸agedevaguesmonochromatiques.Nousavonsfaitvarierleclimatde houlea` traverslefluxd’e´nergiedehouleFetleparame`tredesimilitudede«surf»j.Les diffe´rents processus du cycled’e´rosion de falaise sont identifie´s.L’e´volution dufond de´pendessentiellementduparame`tredesimilitudedesurfj.Desprofilsplansa` pente raide(j>0,7),plansa` pentedouce(0,5<j<0,7)eta` barre(j<0,5)sontobserve´s.Nous avonsobserve´ diffe´rentesdynamiquesdesbarres,notammentdese´tatsstablesetdese´tats oscillantsauto-entretenus.Puisnousanalysonsleroˆledumate´riaue´rode´ surlavitessede re´cessiondefalaise.Nousmontronsquelavitessedere´cessiondefalaiseaugmenteavecle fluxd’e´nergiedehoule.Deplus,pourunfluxd’e´nergiedehouledonne´,elleestplusforte pourunprofilplana` pentedoucequepourunprofila` barre.Cependant,elleestsemblable pourunprofila` barreetpourunprofilplana` penteraide.Lavitessedere´cessiondefalaise n’estpasunefonctionmonotonedelahauteurdefalaise,puisqueletypedeprofildufond influencel’e´nergiedehouleauniveaudelafalaise.

*Correspondingauthor.

E-mailaddress:[email protected](B.Caplain).

1. Introduction

ThecoastlinesoftheEartharecomposedofabout80% ofrockycoasts(EmeryandKuhn,1982).Thesecoastsare composedofeitherconsolidatedorunconsolidatedrocks suchasclay(CollinsandSitar,2008).Itiscrucialtobeable to forecastcliff recession rate as a functionof the local forcingparametersand thedifferentunderlying physical mechanisms should be understood. The main factor controlling clifferosioniswave attack,buttomentiona few others, tidal cycles (Kanyaya and Trenhaile, 2005), lithology, and living organisms (Nesteroff and Me´lie`res, 1967)alsoplayarole.In thiswork,wefocusonerosion controlledbywaveattack.

Wave-driven cliff erosion involves several processes. Thewaveimpactcreatesanotch(Trenhaileetal.,1998)at thebottomofthecliffwhichgrowsuntiltheweightofthe overlyingcliffexceedsthematerialstrength,causingcliff collapse(e.g.Hampton,2002;YoungandAshford,2008). Thiscollapseisresponsibleforcliffretreat andsediment supplytothebeach.Thenwave-drivencollapsedmaterial transportmodifiestheseabedmorphology.Inturn,wave dynamics is changed by sea bed profile evolution (WalkdenandDickson,2008).

DamgaardandDong(2004)performedawetsandcliff erosionexperimentinawavebasinwithaconstantslope. The cliff was locatedon a flat platform.Incident waves weregeneratedwithawavemakerallowingvariablewave incidence. They concluded that the cliff recession rate exponentially decreases in time for normal waves and seems tobe constantforobliquewaves.In addition, the recessionrateincreaseswithwaveheightandperiodand decreaseswithcliffheight.

The aim of the present work is to analyze the cliff erosiondynamicswithinscalescompatiblewith laborato-ryscalebecausesuchinsituanalysisismadedifficultby thelargetimescalesinvolvedinnaturalsystems.Here,the timescaleconsideredisoftheorderofadayandthespatial scaleismetric.Weperformedexperimentsinawaveflume wherethewetsandcliffwaslocateduponaconstantslope (Fig. 1). We will introduce experimental set up and parametersinthenextsection.Thentheself-organization oftheseabedmorphologyisstudied.Then,theinfluenceof thewavepropertiesandsedimentsupplyoncliffrecession rateisanalyzed.Theresultsarediscussedbefore conclu-sionsaredrawn.

2. Experimentalsetup/method

Inthepresentwork,theexperimentswerecarriedout in a 5m-long, 14cm-wide and 25cm-high wave flume whereonlynormalincidentwavesareallowed(Fig.1).The

flume is equipped with a flap wave paddle producing monochromatic waves with a height up to 5cm and periodsbetween0.5sand2s.Theoffshorewaterdepthis d=15cm.Ahardnearshoreslopeoftan(

b

)=1/10isused. Thewetsandcliffisbuiltontheslope(Fig.1)withacliff lengthLc=40cm.Thecliffheighthismeasuredfromthe

free surface at rest tothe cliff top. Calcite sand with a median grain diameter d50=0.41mm and a density

r

s=2.76g/cm3(fallvelocityinwaterofws=5.45cm/s)is

used.Afteracliffdrainageofabout2h,theflumeisfilled uptod=15cm.Thebottomofthecliffissubmergedandan initialnotchappearsduringthefillingofthetank.Then,the wavemakerisactivated.

Free surface position is measured by threecapacitive probes(100Hzsampling)locatedoffshore(Fig.1).TwoPCO 2000camerashavebeenused,oneonthesideoftheflume (withafieldofview1m25cm)(Fig.3cand3d)todetect thewaterfreesurfaceandthebedandcliffpositions,the other one above the flume (with a field of view 40cm15cm) to measure the cliff top position. At the beginningofeachexperiment(for4h),thevideosampling rateisclosetothewavefrequencyasthesystemdynamicsis fast.Thenthesamplingrateisdecreasedtoabout1/10ofthis frequency until the end of the experiment. From video records,thefreesurfaceandthebedpositionsaremeasured. Themonochromaticwave climateis characterizedby two parameters, thesurf similarity parameter

j

and the incidentwaveenergyfluxFwhicharewritten:

j

¼tanffiffiffiffiffiffiffiffiffið

b

Þ

H=L

p (1)

F¼E:cG (2)

withEthelinearwaveenergydensityE=1/8

r

gH2,where

r

isthewaterdensityandgisthegravityacceleration,and

cGthecorrespondinggroupvelocity.Tan(

b

)isthebottom

slope,Hthewaveheight,Lthewavelength.

Cliff erosion rateand bed evolution are studied as a function of incident wave energy, wave shape and cliff height. The conditions of experiments carried out are showninTable1.

3. Results

Atthebeginningoftheexperiments,cliffretreatisvery fast and collapsed sediment quickly creates a sandy platform onthe slope. In case1(reference experiment), theseabedmorphologyrapidlyevolvestoabaredprofile and plunging breaking waves are observed. Afterwards, the sand cliffrecession rate decreasestowards a steady profile(Fig.2).

Fig.1.Experimentaldevice. Fig.1.Dispositifexpe´rimental.

3.1. Bottommorphology

Theinfluenceofthewaveparameters(F,

j

)(Fig.3a)on the sea bed morphology is studied with a series of experiments carried out with the same cliff height

hc=8cm. Three different types of sea bed morphology

aredistinguisheddepending moreon

j

rather thanonF

(Fig.3):

Planarandsteepprofilesfor

j

greaterthan0.7(Fig.3b). Wavesbreakonlywheninteractingwiththebackwashat theoutwardedgeoftheplatform.

Planar and gentle profiles for

j

between 0.5 and 0.7 (Fig. 3c).Waves breakabove the outwardedge of the platform.Spillingbreakersareobserved.

Baredprofilesfor

j

lessthan0.5(Fig.3d).Weobserved either one (case 2)or two (outerand inner) sandbars (cases 1-A, 1-B, 1-C, 1-D, 3 and 4) depending on F.

Breakingwavesareofplungingtypelocatedabovethe outersandbar.

Mostoftheobservedprofilesreachasteadystate(see

Fig.2,forexample).However,somecasesevolvetowards

anunsteadystate.Forexample,case3(F,

j

)=(1.89,0.38) characterizedbyabaredprofileathighenergyfluxshowsa self-sustainedsandbaroscillation(Fig.4a).Aftersometime (7h30min),sandbarsbegintomigrate,landwardforthe outer bar and seaward for the inner bar (Fig. 5). This migration lasts for about 80min. The return motion is fasterandlastsforonly20min.Then,thesystembecomes stableagainforabout1h,beforeanotheroscillationstarts. In sum,the oscillationperiod isabout2h30min.Outer and inner sandbar excursions are about 16 and 5cm, respectively. Another case of a self-sustained sandbar oscillationisobservedforahighercliff(hc=10cm)witha

lower wave energyflux ([F,

j

]=[1.27, 0.39]close to the case1-A).Thesystem dynamicsissomehowdifferentas bar oscillations are in phase and symmetric and the oscillationfrequencyis higher thanin the previouscase (with a period of about30min) but the amplitudes are approximatelythesame(Fig.4b).

3.2. Cliffrecessionrate

We studythe cliffrecession rateas afunctionof the wave parameters (F,

j

) and then as a function of the sediment supply. We seeonFig. 6that fora setof four different realizations ofthe same casein the (F,

j

) plan (cases 1-A, 1-B, 1-C, 1-D) and despite the fact that the collapse eventsare different, the finalcliff positionsare veryclose.Thevariabilityinfinalcliffpositioniscloseto thevariabilityofFforthevariousexperiments(about10%). We thus conclude that the cliff recession dynamics is reproducible in our experiment.The cliff recession rate increases for increasing wave energy flux (Fig. 6a) as observed by Damgaard and Dong (2004). For a given energyflux,wechangedthesurfsimilarityparameter,and thustheseabedmorphology.Cliffrecessionislargerfora gentleplanarprofile(case5:0.5<

j

<0.7)thanforabared profile(case1-A:

j

<0.5)(Fig.6b).Thefinalcliffpositionis the sameforbothabaredprofile(case2:

j

<0.5)and a steepplanarprofile(case8:

j

>0.7)(Fig.6b).

The influence of sediment supply in the system is studiedfromtwoperspectives:

Table1

Experimentalconditions. Tableau1

Conditionsexpe´rimentales.

Cases Surfsimilarity

parameterj Waveenergy fluxF(W/m) Cliffheight hc(cm) Dean parameterV Meanreflection coefficient(%) 1-A 0.38 1.23 8 1.14 9 1-B 0.39 1.17 8 1.10 8 1-C 0.40 1.14 8 1.09 11 1-D 0.40 1.09 8 1.07 10 2 0.39 0.71 8 1.05 6 3 0.38 1.89 8 1.22 12 4 0.46 1.63 8 0.89 11 5 0.55 1.23 8 0.58 18 6 0.56 1.04 8 0.53 12 7 0.56 0.88 8 0.63 12 8 0.79 0.73 8 0.34 34 1–5 0.40 1.12 5 1.07 9 1–10 0.39 1.27 10 0.97 14 6–10 0.54 1.04 10 0.66 9

Fig.2. Spatialandtemporalevolutionofseabedmorphologyforcase 1-A;colorscalerepresentsthebottomelevation(incm).

Fig.2.E´volutionspatialeettemporelledelamorphologiedufondpourle cas1-A;l’e´chelledecouleurrepre´sentel’e´le´vationdufond(encm).

(i)theperiodicremovalofthesandbar; (ii)thevariationofthecliffheight.

Duringa testwhere abaredprofiledevelops(case1:

F=1.19,

j

=0.39),weremoved the outerbara coupleof

minutesaftereachcliffcollapse(Fig.7).Comparingtothe experimentwiththesamewaveparametersbutwithout sandbarremoval(Fig.8),itappearsthatthecliffretreatis moreimportantwhenthesandbarisremoved,featuringan almostconstantrecessionrate.

Thesedimentsupplyinthesystemisalso controlled bycliffheight.Forapproximatelythesamewaveclimate (case 1), weperformed experiments for three different cliff heights (hc=5,8and10cm).Fig. 9shows thatthe

total number of collapse events decreases with cliff height whereas average depth of a collapse event increases, and therefore average volume of a collapse eventincreases.SimilarlytoDamgaardandDong(2004), we observed that for steady bared profiles the cliff recession rate decreases with increasing cliff height (5cm-highand8cm-highcliffs,Fig.10).Inaddition,the same conclusion is reached for gentle planar profiles (case6;hc=8and10cm).

Fig.3. (a)Studiedwavesregimesinthe(F,j)plane;symbolsrepresenttheseabedprofiletype:steepplanar(triangles)orgentle(circles)planarprofilesand baredprofiles(squares).Examplesofsideviewsforeachtypeofprofilesare(b),(c)and(d),respectively.

Fig.3. (a)Re´gimesdehoulee´tudie´sdansleplan(F,j);lessymbolesrepre´sententletypedeprofildufond:lesprofilsplansa` penteraide(triangles)oua` pentedouce(cercles)etlesprofilsa` barre(carre´s).Exemplesdevuesdecoˆte´ pourchaquetypedeprofilen(b),(c)et(d),respectivement.

Fig.5. Seabedmorphologyforcase3atabout7h(greydottedline)andat about9h(blackfullline)(Fig.4a).

Fig.5.Morphologiedufondpourlecas3a` environ7h(lignepointille´e grise)eta` environ9h(lignepleinenoire)(Fig.4a).

Fig.4.SameasFig.2for:(a)(F,j)=(1.89,0.38),hc=8cm(case3)and(b)(F,j)=(1.27,0.39),hc=10cm(baredprofiles);colorscalerepresentsthebottom

andcliffelevation(incm).BlacklinesindicatetheprofilesplottedinFig.5.

Fig.4.IdemFig.2pour:(a)(F,j)=(1.89,0.38),hc=8cm(cas3)et(b)(F,j)=(1.27,0.39),hc=10cm(profilsa` barre);l’e´chelledecouleurrepre´sente

Weobserve, however,that forbaredprofilesthe cliff recession rateis largerfor hc=10cm than forhc=8cm (Fig. 10) so that cliff retreat rate is not a monotonic functionofcliffheight.Weshouldobservehoweverthat, theexperimentwithhc=10cmischaracterizedbya self-sustained sandbar oscillation, unlike other two experi-ments.

We conclude that, as far as the bed morphology is steady, the cliff recession rate diminishesfor increasing cliffheight.

4. Discussion

Weclassifiedthedifferenttypesofbedmorphologyasa function of wave climate. We observed three types of bottomprofiles,planarprofileswitheithersteeporgentle slope and bared profiles which mostly depend on surf similarity parameter value, i.e. on the type of wave breaking.Thewaveenergyfluxdoesnotseemtoinfluence

Fig.7.SameasFig.2,forthecase1withsandbarremoval.

Fig.7.IdemFig.2,pourlecas1,avecpre´le`vementdelabarredesable.

Fig. 9. Histogramof collapse depth for different cliff height (a):(F,

j)=(1.12,0.40),hc=5cm;(b):(F,j)=(1.09,0.40),hc=8cm(case1-B);(c):

(F,j)=(1.27,0.39),hc=10cm.Totalnumberofcollapseevents:(a)30;(b)

9;(c)6.Averagecollapsedepth:(a)0.9cm;(b)2.6cm;(c)4.1cm. Fig.9. Histogrammedelaprofondeurd’effondrementpourdiffe´rentes hauteurdefalaise(a):(F,j)=(1.12,0.40),hc=5cm;(b)(F,j)=(1.09,

0.40),hc=8cm(cas1-B);(c):(F,j)=(1.27,0.39),hc=10cm.Nombretotal

d’effondrements : (a) 30 ; (b) 9 ; (c) 6. Profondeur moyenne d’effondrement:(a)0.9cm;(b)2.6cm;(c)4.1cm.

Fig.6.Timeevolutionofcliffpositionfor(a)differentwaveenergyfluxes and (b) different surf similarity parameters. Initial cliff position is

Lc=40cm.

Fig.6.E´volutiontemporelledelapositiondelafalaisepour(a)diffe´rents fluxd’e´nergiedehouleet(b)diffe´rentsparame`tresdesimilitudedesurf. LapositioninitialedelafalaiseestLc=40cm.

Fig.8.Evolutionofcliffpositionwithandwithoutsandbarremoval.Cliff positionisinitiallyatLc=40cm.

Fig.8. E´volutiondelapositiondefalaiseavecetsanspre´le`vementdela barredesable.Lapositiondelafalaiseestinitialementa` Lc=40cm.

Fig.10.Evolutionofcliffpositionforthreedifferentcliffheights.Cliff positionisinitiallyatLc=40cm.

Fig.10. E´volutiondelapositiondefalaisepourtroisdiffe´renteshauteurs defalaise.Lapositiondelafalaiseestinitialementa` Lc=40cm.

much the type of bed morphology (Fig.3) but only the characteristic length and position of the morphological features.

Beachprofilesclassificationhas beenproposedin the literature basedonthe Dean numbervalue(Wright and Short, 1984). Here,we definethe Dean number

V

with offshorewaveparameters,as:

V

¼ H

T:wS

(3)

Asweuseasinglegraindiameterinourexperiments,

V

evolves similarly as

j

. It means that the bottom morphology depends mainly on the Dean number as observedbyWrightandShort(1984).Steepplanarprofiles are thusobserved for

V

<0.4, gentle planar profilesfor 0.4<

V

<0.8andbaredprofilesfor

V

>0.8(Table1).This dependency of bottom morphology on Dean number is qualitativelysimilartothoseofWrightandShort(1984), althoughtheboundaryvaluesarenotsimilarwhichmay be explained by the different definition of the Dean number,oursexpectedtohavesmallervaluesthantheone ofWrightandShort(1984).

Most of the bottom profiles reached a steady state. Steadyprofileshavebeenpreviouslyobtainedin laborato-ryexperiments(Grassoetal.,2009;Kamalinezhad,2004; Wang and Kraus, 2005). Sandbar migrates onshore for moderatewavesconditionsandoffshoreforveryenergetic waves conditions(Gallagheretal.,1998;Ruessinket al., 2003).Suchmigrationshavebeenobservedinlaboratory experiments (Grasso et al., 2009; Hoyng, 2008), and in nature(CertainandBarusseau,2005).Moreover,unsteady stateshavebeenobservedforbaredprofilesathighwave energyfluxes.Toourknowledge,sandbaroscillationshave neverbeenreportedforaconstantwaveforcing.

Thecliffrecessionratehasbeenstudiedasafunctionof waveforcing.Weobservedthatitincreasesforincreasing waveenergyflux.However,thereisnocleartendencyof theinfluenceofthesurfsimilarityparameteronthecliff recessionrateduetodifferenttypesofseabed morpholo-gy. The sea bed morphology appears as of primary importanceoncliffrecessioncontrol.Interestingly,using numerical modelsDickson et al. (2007) reach the same kind of conclusion that is cliff recession is moderately affected by wave change and strongly affected by the beach/platformmorphology.

Aperiodicremovalofthesandbarleadstoaconstant cliffrecessionrate.ThisresultissimilartoDamgaardand Dong(2004)’sobservationsforobliquewavesleadingtoa constantrecessionrate,inasystemwherethesedimentis removed bytransportationby thelongshorecurrent.For differentcliffheights,weobservedthevolumeofcollapse events increases for increasing cliff height, and cliff recessionrateismoreimportantforsmallcliffsprovided thatthebottommorphologyissteady.Forthetwostable sandbar cases(case 1:hc=5and 8cm),the final eroded

volumesareveryclosewhereasthefinalerodedvolumeis moreimportantfortheunstableprofile(hc=10cm).These

findingsmayindicatethatthebedprofiledestabilization couldberelatedtothecrossingofathresholdvalueforthe erodedvolumeofcliffmaterial.Inadditionitmightshow

that the eroded volume for stable cases is almost independentoncliffheight.

Ifweconsidertheclifferosionalprocessasananalogue to a beach nourishment plan, the results from our experiments may show that an increase of the sand nourishment volume will result in a decrease of beach erosion uptoa certainamountoffilledsand asthe bed profile may become unstable and thus lead to a larger erosionattheend.

5. Conclusions

Wet sand cliff erosion by regular waves has been investigatedin anexperimental waveflume. Our results showthatthetypeofself-organizedsandbedmorphology depends mainly on the surf similarity parameter. Steep planar profiles are observed for

j

>0.7, gentle planar profilesfor0.5<

j

<0.7andbaredprofilesfor

j

<0.5.For bared profiles, we either observed steady or unsteady states in which the sandbars positions oscillate in the cross-shoredirection.

The cliff recession rate depends mostly on the self-organized sea bed morphology. The cliff recession rate increases with the wave energy flux and is larger for a gentleplanarprofilethanforabaredprofilewiththesame wave energy flux. However,it appearsto be similarfor bothbaredandsteepplanarprofileswithaconstantwave energy flux. Thus, the sea bedmorphology considerably influences the hydrodynamics and therefore the cliff recession.Wehaveshownthatthesedimentsupplyplays an importantrole oncliffrecession givingsome insights intonourishmentstrategies.

Acknowledgments

We gratefully acknowledge PRES Universite´ de Tou-louseforitsfinancialsupport,aswellasInstitutNational desSciencesdel’Univers(INSU)andSHOM(‘‘reliefsdela Terreprogram’’),foradditionalfundingofthe‘‘Rockycliff erosion’’projectleadedbyV.R.WealsothankSergeFont, Se´bastienCazinandHerve´ Ayrollesforvaluabletechnical assistance.

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