Re-study on Recurrence Period of Stokes Wave Train with High Order Spectral Method

(整期优先)网络出版时间:2011-04-14
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OwingtotheBenjamin-Feirinstability,theStokeswavetrainexperiencesamodulation-demodulationprocess,andpresentsarecurrencecharacteristics.StiassnieandShemerresearchedtheunstableevolutionprocessandprovidedatheoreticalformulationfortherecurrenceperiodin1985onthebasisofthenonlinearcubicSchrdingerequation(NLS).However,NLShaslimitationsonthenarrowbandandtheweaknonlinearity.Therecurrenceperiodisre-investigatedinthispaperbyusingahighlyefficientHighOrderSpectral(HOS)method,whichcanbeappliedforthedirectphaseresolvedsimulationofthenonlinearwavetrainevolution.ItisfoundthattheStiassnieandShemer’sformulashouldbemodifiedinthecaseswithmostunstableinitialconditions,whichisimportantforsuchtopicsasthegenerationmechanismsoffreakwaves.AnewrecurrenceperiodformulaispresentedandsomenewevolutioncharacteristicsoftheStokeswavetrainarealsodiscussedindetails.