breaking wave design criteria

7/30/2019 breaking wave design criteria

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CHAPTERTWO

BREAK INGA V EES IGNR ITER I A E.B. Thornton (M .SCE )1,C .S . W u (M .SCE)1,R . T . Guza2

ABSTRACTBreakingaveeightsmeasured inothieldndandomave laboratoryxperimentsrexamined. Theependencefreakereightandreakerepthneach slopendeepwaterteepnesssresented.TheesultsreomparedwithheesignurvesfhehoreProtectionManua l (SPM)ndheredictions ofheandanaveodel byoda(1975). Theomparisons indicatehatheignificantreakereight,basednoda'smodel, isslightlyonservativeorhexperimentalcases;uthemaximumreakereightsreeasonablyredicted byhemodel. Theesign proceduresnheP Mreasedn monochromaticwavereaking,ndppearverlyonservative, particularlyorow waveteepnesslesshan.01)whichccurrequentlynheWestCoa s tfheUnited States. ThesefheRayleighdistributionopredictaveeightstatistics isestedwithandomaveataorothdeepndhallowwateregions.

INTRODUCTION Theelectionfreakingesignavessssential forheesignof oastal structurerorheoastal sedimentroblem. Th epresentesign practicesopecifymaximumreakingavesasednempirical curveserived primarily from laboratoryxperimentsfmonochromaticaves (constanteriodndaveeight). Severalconcerns arise fromsingmonochromatic laboratoryaveatas asis

forrototypeesign. Uncertaintiesxistnhecalingfaboratorywavesoherototype. Moremportantly,avesnaturereotmonochromatic but random,aving variableeriod,eightndirection.Thebse rvedea nreakereightorandomavessenerally0-40% be lowhereakernceptioneightoreriodicaves . Hence,uncertaintyxistshenpplyingriterionasednmonochromaticavestoctual conditions inature.Thebjectivesfhisaperreo synthesizevailable random wavexperiments, bothnheieldnd laboratory,ndoomparehe

'DepartmentfOceanography, Na v a l PostgraduateSchool,Monterey, C A39432Shorerocessesaboratory, Scrippsnstitutionfceanography-A009,UniversityfCalifornia,aolla, Califronia2093

31


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32OASTALENGINEERING -1984resultswithheandomaveodel ofotia (1975)ndhereakingave design curvesnhehoreProtectionManua l (U SrmyorpsfEngineers, 1977).R A N D O MA V EA T A

Duringheastecade ,hereaseen rowing recognitionhatsignificantifferencesxiste tweenheesultsfmonochromaticndrandomavexperiments. A theameime,rimarilyueoetterinstrumentation, largeumberfomprehensiveearshoreieldexperimentsave beenonducted. Adifficultynynthesizingariousexperiments, particularlyheieldata,shatheatae re collected indifferent anners . The requirementsornclusionnhedataaseerere: 1)heavesreandom,ithermeasurednhefieldrimulated inheaboratory; 2)heatareorissipative,progressiveavesnelativelylaneloping,nbarredeaches ; 3 )hewaveeasurementocations belosenoughoccuratelyefinehepositionfheea nreakingaveeight;)heataeivenntermsfithersignificanteight, H1/3,rmaximumeight, H max.Basednheboveequirements,woetsfieldataollectedndertheearshoreed imen transportStudies (NSTS )ndwoetsflaboratoryxperimentsnavehoalingrencludednheresentpaper.Torreyi neseach , S anDiego,California. TheeachndnearshoretTorreyPineseach isentlylopingwithearlyarallelandlaneontours. Duringhexperiments, significantffshoreaveheightsariede tween0nd60m. Theve rageeak frequencyfthencidentavepectraaried littleuringhexperimentsndasabout.07z . Shadow ing byffshoreslandsndffshoreefractionlimithenglesfave incidencen0-mepthoesshan5. Itwashownyuzandhornton1980)hatecausefhemallincidentngles, refractiveffectsaneeglected inalculatingshoalingrocesses. Theonditionfearlyormallyncidentspilling(ormixedlunging-spilling)aves , breaking in ontinuousaycross

theurfone,revaileduringostfhexperiments. Windsuringthexperimentse reenerallyightndariablenirection.Surfacelevationndorizontal,rthogonal velocityomponen tse re measuredysing loselypacedrrayfpo7 instrumentsnshore-normal transect fromffshorethe0-mepthontourocrosstheurfoneseeFigure nhorntonnduza1983]).Leadbettereach , S an t aarbara,California. Theea nearshoreslopeteadbettereacharied be tween.017nd.05uringheexperiment,ependingnheavelimate. N offshorearasapparent. Thehorelineashenusua l east-westrientationlongpredominantlyorth-southoast. Thepenceanavesreimitedonarrow i ndowfpproach (+9enteredn70)ecausefheprotectionro mPointConceptionoheorthndhehanne l Islandstoheouth. Theenerallyighlyilteredceanwell typeavesfromlmostuewestmustake ightngleurnopproachheeach normally. As esult,avespproachtargebliquenglesohebottomontours inheurfonend drive trong longshoreurrent.


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BREAKINGWAVEDESIGNCRITERIA3Becausefheelativelyargencidentavengles, refractiveeffectsmus teccountedornhehoalingalculations. AimilararrayohattTorreyPinesasse doeasureheaveeighttransformationro m-mepthohehorelineS eehorntonnduza ,1984).

Laboratoryxperimentsyoda (1975)ndERC. Goda (1975)conducted eriesfxperimentsn 0 ong laboratoryavelumeusing randomaves . Twoeach slopesf.02nd.1e resed.Differentavepectrae remployedimulating singleeaked in d waves , doupleeakedeand swell superposed,arrowwellaves ,ndrelativelyroad bandedaves . W a v eeightserealculatedtixlocations spann ingheurfone . Randomaveaboratoryxperimentswerelso performedtE R Cnd have beenariouslyescribedySeeligetl_1983),hompsonndincent1984),ndVincent1984). Theplaneottomlopeas:30n 5.7 ong tank. Measurementse re madetineocations. Variousheoretical wave spectraere simulated, includinghePierson-Moskowitz,O N S W A PndOchi-HubbleSpectra.

Theaveeightstatistics ofPIT1S,Hj/3rH^xerealculatedusingheero-up-crossechnique. Theurfacelevations forhefieldataereirstand-passiltered (0.05-0.5z). Goda (1975)uses^/260rm a x >hich isssentiallyheame statistic. Allstatisticsreompared (nondimensionalized) usingheeepwatersignificantave height0ndeep waterwaterave lengthefinedsL0 (g/27r)Tp2,hereporresponds toheave periodtheeak ofthepectrum. Deepwateraveeightserealculatedyranslatingtheeasuredearshoreaveeightsoffshoreccountingorhoalingand refractionsing linearaveheory. Forheataonsidered,refractiveffectsreeededoeccountedornlynhean ta Barbaraata.Monochromaticavesreakn laneeach atssentially inglelocationwith onstantreakereight. Hence, breakereightnd

depthreunambiguouslyefined. Inontrastomonochromaticaves ,theresowell-defined breakpointorandomaves ;heargestavestendoreak farthestffshorendhemalleravesloserohore.The result is patial distributionfreakingndnbrokenaves .Howeve r ,tsoundhathesef impleerminologyordescribingreakingave parameters isnformativendimplifiesheanalysis. Forhiseason,entroduce eanreakerineorandomwaves . Ameanreakerine"sefinedsheea nocationhereheave ragedaveeighteaches itsmaximumsheavesh o a l fromeepwaterndhenissipateueoreaking. Asnxample,hemsave heightsmeasuredtorrey P i n esrehown inigure. Theea nms breakereightRnd surfonewidthgreefinedherermseachesaax imum. Similarstatisticsreefined for1/3nd H ,ax,ndnexample ishownnigure. Thisdefinitionfeanreakereightmeanshathermsnd H]/3statisticreadepfrokennd unbrokenaves . Themaxstatistic


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34 COASTALENGINEERING-1984

u.o"B /

" ~ ~ ~ -^ 0.6 ^0.4

0.2

. r i 1 i i i 1 i000 20000X(m) 400

Figure. Definitionfea nreakingaveeightB,ndcorrespondingurfonewidthR .

2 -

. uMA X/ ^A/ Hl/3

_ j/ y* --* fyis^/tlt1 H o

02x/xbFigure2 .aveheightstatisticsHmax>H 1y3,andHrmsnormalizedb ydeepwatersignificantwaveheightH0,a sfunctionso fdistanceoffshore.


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BREAKINGWAVEDESIGNCRITERIA5 correspondsoheingle largestaveeasureduringhexperimentalinterval andresumablyorrespondso reaking,rncipientbreakingave .

Thedifficultyfsinghisdefinitionorea nreakereightsthatmeasu remen tocations needoeloselypacedoccuratelylocateheointfhemaximumaveeight. Also,nomefheatathereppearedoeomaximum;hisesultccurred forothhefieldndaboratoryatawherehebviouslamenefractiveeffectsreotresent).RESULTS

Thereakingaveeightatareomparedwithreakingave designurvesalculated bySeelig (1979),homploysheandomave heightransformationheoryyoda (1975). Goda ' sheoryescribestheaveeightssing modifiedRayleighdistributionnwhichhetail ofhedistribution ishortened, supposedlyo representhedecrease inaveeightueoreaking. W a v eransformationsdescribed usingheonlinearheoryyhu to (1974). BreakereightisxpressedyJb A-W-exp(-1.5.JL[i Ktan)])] 1)Hooowhe r e shereakingaveeight, sheocal depthndan istheeachlope. Thereakingaveeightsreescribedsaryinglinearlyver angefaluesro mostrequentreakereightomaximumreakereightependen tnheoefficient (0.12,.18),andtheroefficients 5nd s /3. Theoefficientalueswereuggestedyoda (1975). Goda ' sheoryredictsheho reward transformationfhedistributionnon-Rayleigh)faveeights,including bothrokennd unbrokenaves , accounting forave growthdu eo shoalingndttenuationueoreaking.

Seelig1979)se doda 'sheoryoalculatehemeanreakerheight"ndreakerepththatocation.eeligefinedheea nrandomreakingaveeightnheameannersse doefinehebreakerineorheata,.e.heocationfheaximumaveeightinhehoalingransformationfheavesro mffshoreohee a c h .Seeligalculated eriesfandomavereakingesignurvesorvariouseachlopesnd initial deepwateraveteepnesses.Theignificantreakingave heights, H1/3,reomparedorvariouseachlopesnigure. Laboratoryatarendicatedyopenymbo lsnd fieldataylosed symbols. Theieldataa ve loweraveteepnessueoheredominantlyowrequencyPacific

swell (.07z)hatrevaileduringheieldxperiments.TheurvesySeelig,orrespondingoeach slopes.1,.05nd0.01,rehownsolidines. TheP Mreakingaveesignurvebasednmonochroma t i caveataoreach slope.02sresentedor


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5.0

4.0oX 3.0

> 2.01.0

0.0

A * > *

S LOPE A020o033Q05000

_i1 0 " 1 0 " 2

H0/L 1 0 " Figure. Significantreakingaveeight, H1/3 ,s unctionfdeepwateraveteepnessndeach slope. ShownreSeelig (1980) design curvesoreachl opes.1,.05,nd.0 1asedno d a (1975 )theory (solid lines)ndP Murveoreach slope.02dashedine).

oX

5.0

4.0 -

3.0o E 2.0

1.0

0.0

-A O O

SLOPE.020.033.050.100

-^-A *

A A ^ ;

^~^-S3^^^~-_ _o '0rrz.05.01

1 1 1 1 11 0 " 10" '

H0/L 1 0 " Figure. Maximumreakingaveeight, H max,waterteepnessndeach slope. a s unctionfee p


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BREAKINGWAVEDESIGNCRITERIA7 comparisondashedine). TheP Murve islatter,utenerallyfallswithinhe rangefheSeeligurvesorandomaves .

TheSeeligurveseasonablyredictheteeperave slopelaboratoryata. Thissxpected sinceheoefficientsse d in1)specifyingoda 'sheoryreasednheame laboratoryatacollectedyoda. B u theurvesverpredictheignificantreakerheightsornitiallyowlopeaves . Therefore,heSeeligurvesappearo reasonablyredict significantreakereightsornitiallysteeperaves (H0/L0 .7X10"^),utppearverlyonservative forpredicting significantreakereightsornitiallyowteepnesswaves .

TheaximumreakingaveeightsreomparedwithheSeeligdesign curves inigure. Theurvesive reasonableredictionsfmaximumreakingaves ,lthoughheataootlignwellwithhebeachlope dependencefheurves. Itsointeduthatorhelowaveteepnessata,hemaximumaveeightsomparewellwiththatyoda 'smodel,he reasheignificantaveeightsreover-predicted. Thissortuitous. The reasonshathectualwave heightsonformoreloselyo RayleighdistributionhanRayleighdistributionwith hortenedail. Theodamodel,mployingamodified Rayleighdistributionwith hortenedail,redictssmallerncrease inaveeightrcm H1/3omaxhanheata,othatheH^xurvesoot overpredict theeasured valuessuch .

Thorntonnduza (1983)howedhatorheorreyPinesataheRayleighdistributionouldese doalculatehemaxwithn averagerrorf7% (under-prediction). Compar i sonsfhean ta BarbaraatawithheRayleighdistributionrehown forHj/3nFigure ndorH^xnigure. TheRayleighdistributionredictsH1/3 .41rms 2)

Figure howshatmos tfheHj/3aveeightslotteds unctionofepthallwithin5 % (dashed line)f (2). Theaveeightsndeeperwaterdepth )ppearogreeetterwithheRayleighdistributionhanaveeightnhallowerwaterwithinheurfon e .ThemaxatandaluesredictedrcmheRayleighdistributionrecomparednFigure. Theve ragerrorfheegressionurve(dashed line) f romhe5 ines9% , i.e.,heRayleighdistributionunder-predictsheatay%nheverage,lthoughhecattersconsiderablyreater. ThismplieshathesefmodifiedRayleighdistributionwith hortenedail asescribed byoda (1975)opredict breakingaveeightesign conditions isonconservative; itiso und fromield easu remen tshathesefRayleighdistributionislsoonconservative.Theepththeignificantreakingaveeight,^,, islotteda s unctionfaveteepnessnd beach slope inigure. Aeach slopeependencesvident. TheatareeasonablyepresentedytheSeeligurvesndrenlynderestimatedtheeryowestavesteepnesses.


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2.00

1.75

1.50

1.25

1.00

DATEn 2020 302f\ 402+ 502X 6020 1302V H02H 1602X 1702

Dep t hm) 10 Figure. Significantav eeights, H\/3,easuredtantaarbara,Californiaomparedwithaveeightredicted byRayleighistribution(solid line)s unctionfepth. Dashedines indicate5 %rror.

Xo

250r200

150 -100

50

50 100 150 200HmaxRayleigh) 250Figure. Maximumaveeights, H m measuredtantaBarbara,Californiaomparedwithaveeightredicted byRayleighdistribution. Meanegressioninesndicatedyashed line.


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BREAKINGWAVEDESIGNCRITERIA 39

5.0

4.0

x 3.0

T?.01.0 0.0

- SLOPE .* *_ M

A .020o .033 .050o 100

" " ^^v o ..01- S\B^ O T -- jf^.05

,.100 0 0

1 1 1 1 1 1 I I1 0 " ,-21 0

H0/L 1 0 " Figure. Dep thtignificantreakingaveeight,j,,sfunctionfaveteepnessndeach slope.


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40OASTALENGINEERING-1984S U M M A R YN D CONCLUSIONS

Breakingaveeightseasured inheieldnd inandomave experimentsnheaboratoryreomparedwithheandanaveode lofoda (1975)salculated bySeelig (1980)ndwithhehore Protectionanua l (1977). Theandomaveode l suggestshatavebreaking isependen tneachlopendaveteepness. Theataspans aangefeach slopes (0.02, 0.033, 0.05nd.10)ndeepwateraveteepness. Theependenceneachlope is, however,otobviousro mheata. TheaboratoryatarefigheravesteepnessH0/L0 .7X10"3). Theieldataorrespondsoowave steepnesssheesultfowrequency (.07z) Pacificceanwellwaves .Theoda'sodel reasonablyredicts^/3nd h^axorheigherwaveteepnessaboratoryata; reasoneinghatuchfhelaboratoryatasakenro moda (1975),hich isheameatase dtoalibrateheandomaveodel inheirstlace. Fo rnitiallylowteepnessaves ,heodaodel overpredicts2/3,utore reasonablyredictsmax. Themaxredictionsreasednsingmodified,hortenedail,Rayleighdistributionorwhichhemax statisticsreompensa ted foryheoverpredictionfH1/3. Actualshallowwaterave heightataompareetter,rreven underestimated inheail,with Rayleighdistributionssdemonstratedwithheieldata. Breakingaveeightsoo t exhibitahortened orruncated,ail inheirdistributions.

Theepthtreakingorrespondingohereakingaveeightcompared favorablywithheodaodel forallave steepnessalues.Depthtreakingxhibited adefiniteependenceneach slopessuggestedyheodaodel andheata.A C K N O W L E D G E M E N T S

Thisesearch wasupported byheOfficefava l Research,Coastal Sciencesranch, unde rontractumbersR88-114(E.B. Thornton),ava l Postgraduatechoo l FoundationC.S. W u )ndN00014 -75 -C - 0300R.T. Guza). Much ofhenalysisaserformed by D.O. Burych.REFERENCES Goda ,Y., "Irregularaveeformationnheurfone",CoastalEng ineering inapan8, 13-26, 1975.

Gu z a ,R.T.nd.B.hornton,Localndhoa l edompar isonsfea SurfaceElevations,ressuresndVelocities",.fGeophysicalResearch,5, 1524-1530, 1980.Seelig,W.N., "MaximumWave HeightsndCritical WaterepthsorIrregularavesnheSurfone", Reporto. 80-1,.S . ArmyorpsofEngineersCoastal Engineering Resea rchCenter,1., 1980.Seelig, W.N.,.P. Ah r en snd .G .Grosskopf, "TheElevationndDurationfa v eCrests", Reporto. 83-1,.S . Armyorpsf

EngineersCoastal Engineering ResearchCenter, 73., 1983.


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BREAKINGWAVEDESIGNCRITERIA1Shuto,N., "Nonlinearongavesn h an n e l ofariableection",Coastal Engineering,napan,17, 1-12, 1984.Thompson,.F. andC.L.Vincent,hallowWa te rWaveeightParameters",. a te rway ,Port, Coastal andceanngineeringDivision,S C E,110 , 293-298,ay ,984.Thornton, E.B.nd.T . G u z a , "Transformationfa v e HeightDistribution",. ofGeophysical Resea rch,, 5925-5938, 1983.Thornton, E.B.nd.T . Gu z a , "LongshoreCurrentueoandomWaves " ,(Submittedohe.fGeophysical Resea rch) 1984.U . S . Armyorpsfngineers, Sho r eProtectionanua l,CoastalEngineering Resea rchCenter,977.Vincent,C.L., "EnergySaturationfrregularWavesDuringShoaling",(Submittedo. Wa te rway ,Port, Coastal andceanngineering,Division,SCE) 1984.

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