Fifty Years of Wave Growth Curves

7/28/2019 Fifty Years of Wave Growth Curves

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FiftyYearsofWaveGrowthCurves1PaulC .Liu 2

AbstractIthasbeenoveriftyyearssincethepublicreleaseofthewell-knownmonographofNavyH.O.601,preparedbySverdrupandMunk(1947)duringWorldWar

I I .nelebrating0 t hnniversaryfheInternationalCoastalEngineeringConferencethatwasstartedin1948,itisofinteresttorevisitthewavegrowthcurvesdevelopedinH.O.01andcomparethemwitharecentstudyonwavegrowthcurvesDonelaneta1.992).tisclearthatwhilesignificantprogresshasbeenmadeoverheast0years,verdrupandMunk'soriginalideastillprevailsinlightofmoderndevelopments.IntroductionThemid yearsofthedecadeof1 9 9 0sobservemany50thanniversariesofeventsthatrelatetotheendofWorldWarI I .heendofthewarmarksthestartoftwo

importanteventsthatareofinteresttocoastalandoceanengineers:hepublicreleaseofthewell-knownmonographoftheNavyH.O.01bySverdrupandMunk(1947)andthebeginningoftheInternationalCoastalEngineeringConference.hesetwoeventspracticallyusheredinthemoderneraofwindwavestudies,andonthisSilverConferenceofICCEitisinterestingtopayaeturnisitoverdrupndMunk'saverowthcurvesgiveninH.O.601andtocomparethemwiththe"GLERLContributionNo.1034NOAAGreatakesnvironmentalesearchaboratory,Annrbor, MI 48105-1593. Email: [email protected]

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458 OASTALENGINEERING996recentstudyofwavegrowthcurvesgivenbyDonelanetal.1992).hispapersummarizestheessentialsofthedevelopmentofthetwogrowthcurves50yearsaparttoshowthedifferencesingeneralapproachesandthesignificanceoftheconceptualbasisofH.O.01thatprevailsverimendtillppearsefreshingnlightofmodernachievements.TheWaveGrowth CurvesAccordingtoSverdrupandMunk

Whenverdrupndunketutoeveloptechniquesforwaveforecastingintheearly1 9 4 0'sinsupportofU.S.amphibiousoperationsduringWorldWarI I ,thestateofknowledgeatthetimewasbasedmainlyonempiricalrelationships.otableresultssuchasthataximumaveeightsreroportionalohesquareootfheetchndhataveeightsproportionaltothewindspeedorthesquareofthewindspeed,alldependentondimensionalconstants.

SverdrupandMunkstartedtheinitialeffortstorealisticallymodelhewindwavesbyexamininghegrowthofwavesonthebasisofenergyconsiderations..Theyformulatedthefetch equation as

cdE Edc T~+r=R,+K2dx 2dx whereEsthemeanenergyperunitsurfacearea,cisthewavephasepeed,ndRtndRvrehenergytransferredtothewavesattheseasurfaceduetothetangentialtressndormalressurefind,respectively.

ByformulatingthephysicalconsiderationsofRtandRVIncorporatingmeasuredinformationavailableatthetime,ndnormalizingsignificantwaveheight,H ,wavephasespeed,c ,andfetch,x ,withwindspeed,U ,andgravitationcceleration,,heywerebleoderivenalyticalxpressionsordimensionlesswaveheight,gH/xf,anddimensionlesswavespeed,/U,thewaveage,)asfunctionsofdimensionlessfetch,gx/U2.


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WAVEGROWTHCURVES 59

Inssenceheyocusednhewoasicparameters,thewaveage 3 =c/Undthewavesteepness8/L,sheaveength,herempiricalfunctionalrelationshipsbetweenthetwocanbededucedfromtheabovefetchequation.heythenderivedthreeseparateexpressionsforgx/lfntermsof ?and8 overthreedividedrangesofp.aveheightrelationswerehenbtainednheimensionlessormromlineartheoryas

= 2#= /(^;Followingheseevelopments,heinalnalyticalexpressionsgiveninH.O.01alsoncludednolessthan1 7empiricalconstants.hesegrowthcurvesareplottedinFigure1asthinsolidlinesalongwiththehistoricaldataoriginallyused.ThedevelopmentsofSverdrupandMunkclearlysetthestageformodernwindwavepredictionandstudy.Theirinnovativeintroductionoftheconceptofsignificantwavesasedonstatisticalconsiderationsisstillthemostasicndffectivearametersedncharacterizingaveieldarameters.neightconcludehatslsoartfverdrupndMunk'sinnovations.owever,hesefimensionlessparameterswasactuallysuggestedtoSverdrupandMunkbyMorroughP .O'Brienbasedonintuitiveunderstandingofluidmechanicsndknowledgefimilitudendmodellaws2WiegelandSaville,996.)hepracticeofcorrelatingdimensionlessparametersgH/xfndc/Uwithrespecttogx/lfstillwidelyusedtodayaspartfheasicnalysisfindndavemeasurement.2TheauthorisindebtedtoProf.iegelforpointingoutthisimportanthistoricalfacttohim.


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460 COASTALENGINEERING99 6

10u-iDonelanetal.(1992)

10-1-S-

10-2-

10-3-'"Jonswap, >^C-Mitsuyasu,etc.a/C-


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WAVEGROWTHCURVES 61

An OdetoH.O.601

SverdrupndMunkpreparedhe.O.01hatestablishedhehysicaloundationsorindavepredictionsandsubsequentwavestudies.retschneider(1952)madefurtheranalysiswithadditionaldataanddevelopedpracticalcurvesthatbecamethewidelyusedSMBSverdrup-Munk-Bretschneider)ethodfaveforecasting.it htheadvanceofspectrumanalysisinthe950'sndncreasingsefomputersnhe1960's,alongwithnewinstrumentationandmeasurementtechniques,ewapproacheshavesubsequentlyevolved.ButthebasicprinciplesimplementedinH.O.01havebeencontinuouslypracticed,somemaybeunwittingly,bymostfheaterindavenalysisndodeldevelopments.

Hasselmann(1984)inanarticlethatpaystributetoWalterMunk's5thbirthday,ntitled"AnOdetoH.O.601,"presentedacomparisonoftheH.O.601growthcurveswithmoderndataofJONSWAPprogram(Hasselmannetal.,973)andMitsuyasu(1969)asshowninFigure1 .HecommendedthelegacyofH.O.01andconcludedthatTherogressneasurementechniquesasclearlybeencommensuratewithheprogressnwavemodeling."orerecentmodelingdevelopments(Komental., 1994)appeartosubstantiatethiseffect.TheWaveGrowthCurvesofDonelanetal.

Theworkofonelanetl.1992)rovidesninterestingaccountofthecurrentstateoftheartoftheaverowthurvetudies.heyxploredhefetch-limitedwindwavegrowths,singthewindandwavemeasurementsfromalineararrayoffivetowerslocatedlongheprevailingwinddirectionnheeasternhorefaket.lair,ndoundhedifferentialgrowthofspectralwaveenergy betweenthetowers, AEIAx,obealinearfunctionoflocalwaveage,UIcp,here shewindspeed,ndphephasespeedofthewavesatthespectralpeak as:


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462 COASTALENGINEERING99 6

AE -0 . 7 8 x 1 0 "2gEAx - 0 . 8 3Notethattheright-handsidevanishesatUIcp= 0 . 8 3 ,whichishewell-establishedconditionforaullydevelopmentwavefieldPiersonandMoskowitz964.)Nowcombiningthedifferentialequationwiththatofthe well-known empirical relation betweennondimensionalnergy,= g2EIU4 ndavegesubstantiatedbymostfhemeasurementsmaderommany partsoftheworld:

= 0 . 0 0 2 3ucVPJreadilyyieldsthefollowingfetchrelations:

andX = 4 . 0 9 4 6 xlO 4 I nl - 5 , 5 4 1 4 e 3 - 2 . 2 6 9 0 x1 0

s l + 2 . 7 7 0 7 e 3

X*=4 . 0 9 4 6 xlO 4 I nU _

U - 0 . 8 3 0 2 3 . 3 9 9 2 x 1 0 ' U

- + 0 . 4 1 5 1

where isheondimensionaletchx/U hecorrespondingresultsofthesetwoequationsarealsoplottedasthethicksolidlinesinFigure1inwhichH*=Ag4elU1 andT*=cpIU areusedtofacilitatethecomparisonit hriginal.O.01urves.nexaminationofFigure1indicatesthattheresultsofDonelantal.1992)reowerhanhe.O.01curves,butreachthefullydevelopedstagemuchlater.


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WAVEGROWTHCURVES 63

Ineneral,owever,hileat aeasurementndanalyticmodelinghavemadesignificantprogressoverthepast50years,theingenuityofSverdrupand Munk'soriginaldevelopmentwithverylimitedavailabledatanotnlyhelpedheAlliedorcesuringheNorthAfricaoperationsthatledtoWWIIvictory,butalsoremainedeasonablyloseoheodernndatestmeasurements.ConcludingRemarks

Forheostart,heaverowthurvedevelopmentsofSverdrupandMunkandthatofDonelanetal.1992)reasicallyimilar.ot hrebasicallytartednvailableeasuredesultsfollowedbyanalyticalderivations.it hlimiteddataSverdrupandMunk'sdevelopmentrequired17constantsfortheoperation.onelanetal.,owever,withmuchmoreandbetterestablisheddataandanalysisreliedonfourempiricalconstants.hecurrentstateoftheartofwindwavemodelingasgiveninthecomprehensivebookyomen1994)autionedhatDespiteheprogress,etillreotbleoakeavepredictionsthatalwaysfallwithintheerrorbandsofthebservations."tppearshatfter0yearsdevelopmentand progressonwavemodelingand windwavestudies,hileaveodelingechniquesaveadesignificantprogressforpracticalapplications,hereismpleoomfurtherrogressndnhancementremaintobeexplored.


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464 OASTALENGINEERING996ReferencesBretschneider,.L . (1952),Revisedwaveforecastingrelationships,roc. ,ndConf.oastalEng, CouncilWaveResearch,ngineeringFoundation,Berkeley,CA,1-5 .Donelan,..tal.1992),nthegrowthrateofwind-generatedwaves,Atmosphere-Ocean,3 0 ,457-478.Hasselmann,.1984),hecienceandartfwaveprediction-AnodetoHO601,nAelebrationnGeophysicsndOceanography 982,crippsInstitutionofOceanographyReferenceSeries84-5,31-37.Hasselmann,K .etal.1973),Measurementsofwind-wavegrowthndwellecayuringheointortheaProject(JONSWAP),eutscheHydrogr. Z.,1 2 . Komen,.J.tal.1 9 9 4 ) ,DynamicsndModellingfOcean Waves, CambridgeUniversityPress,532p.Mitsuyasu,.19 68/ 19 69 ) ,nherowthfhespectrumofwind-generatedwaves,ep.es.nst.Appl. Mech.,KyushuUniv.,16/17.Pierson,..ndL .oskowitz1964) , proposedspectrumformforullydevelopedwindseasbasedonsimilaritytheoryofS .A .Kitaigorodskii,J.eophys.Res., 6 9 ,5181-5190.Sverdrup,H .U .andW .H .Munk1947),Wind,eandSwell:heoryofelationsororecasting,.S .NavyHydrographicOffice,H .0 .Publ.No.601.

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Fifty Years of Wave Growth Curves