{"title":"Second-order Stokes wave solutions for gravity capillary water waves in three-layer dendity-stratified fluid","authors":"Yan Zaizai, C. Wei, M. Ren","doi":"10.7498/APS.63.140301","DOIUrl":null,"url":null,"abstract":"The gravity-capillary water Waves in two-layer density-stratified fluid are investigated by using a singular perturbation method,and the third-order asymptotic solutions of the velocity potentials and the third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory.As expected,the third-order solutions describe the third-ordei;nonlinear modification and the third-order nonlinear interactions between the interfacial waves.The wave velocity depends on not only the wave number and the depths of each layer,wave amplitude but also the surface tension.","PeriodicalId":18427,"journal":{"name":"Mathematics in Practice and Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics in Practice and Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7498/APS.63.140301","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
The gravity-capillary water Waves in two-layer density-stratified fluid are investigated by using a singular perturbation method,and the third-order asymptotic solutions of the velocity potentials and the third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory.As expected,the third-order solutions describe the third-ordei;nonlinear modification and the third-order nonlinear interactions between the interfacial waves.The wave velocity depends on not only the wave number and the depths of each layer,wave amplitude but also the surface tension.
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