homotopy+analysis+of+nonlinear+short-crested+waves+in+water+of+finite+depth

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1、Homotopyanalysisofnonlinearshort-crestedwavesinwateroffinitedepthP.Wang1,2andD.Q.Lu1,3,∗1ShanghaiInstituteofAppliedMathematicsandMechanics,ShanghaiUniversity,YanchangRoad,Shanghai200072,China2CollegeofMathematicalScienceandPhysics,QingdaoUniversityofScienceandTechnology,99SonglingRoad,Q

2、ingdao266061,China3ShanghaiKeyLaboratoryofMechanicsinEnergyEngineering,YanchangRoad,Shanghai200072,ChinaAnanalyticapproximationmethodknownasthehomotopyanalysismethod(HAM)isappliedtostudynonlinearshort-crestedwavesinwateroffinitedepth.Seriessolutionsforthevelocitypotential,thewavefrequenc

3、yandthewaveprofilearederived.Thecalculatedpropertiesofshort-crestedwavesagreewellwithpreviousnumericalresultsforsmallwavesteepnessandwiththeincreaseofwavesteepnessoursolutionsappeartobemorepronounc-ing.Furthermore,HAMprovidesaconvenientwaytoguaranteetheconvergenceofseriessolution.Thiswork

4、indicatesHAMissuitabletosolvenonlinearshort-wavesproblems,especiallythosewithoutsmall/largephysicalparameters.Keywords:Homotopyanalysismethod(HAM),Three-dimensionalwaves,Nonlinearshort-crestedwaves,Waveprofile.1.INTRODUCTIONThetheoryonshort-crestedwaves(SCWs)wasfirstdevelopedbyFuchs(1952)

5、[1],whoob-tainedasecond-ordersolutionthroughaperturbationtechnique,whereasChappelear(1961)[2]extendedittothethirdorder.However,thetwosolutionswerenotapplicableforthelim-itingconditionofSCWs,i.e.progressiveandstandingwaves.Hsu(1979)[3]introducedthewavesteepnessεasasmallperturbationparamet

6、erandrevisitedthethird-ordersolutioninanon-dimensionalform,includingprogressiveandstandingwaveslimits.BasedonthesolutionproposedbyHsu(1979)[3],Fenton(1985)[4]furtherstudiedthewaveforcesandpressuresonverticalwall.Later,Teo(2002)[5]extendedtheanalyticalsolutiontothefifth-ordersolutionforSCW

7、s.Recently,Jian(2009)[6]investigatedthepatternsofcapillary–gravitySCWswithauniformcurrentandobtainedthethird-orderapproximatesolutions.Huang(2011)[7]derivedanalyticalsolutionsforpartiallyreflectedSCWsbyaverticalwallbreakwater.Asweknow,theperturbationmethodisextensivelyempl