两层密度分层流体毛细重力波三阶Stokes波解  

Third-order Stokes Wave Solutions for Gravity-Capillary Water Waves in Two-layer Density-stratified Fluid

作　　者：崔巍[1] 陈小刚[1] 木仁[1,2] 沈玉艳[1] 郭军明[1] 包曙红[1] 

机构地区：[1]内蒙古工业大学理学院,内蒙古呼和浩特010051 [2]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《数学的实践与认识》2011年第17期126-132,共7页Mathematics in Practice and Theory

基　　金：内蒙古工业大学科研计划项目(ZD201034);内蒙古大学"211工程"创新人才培养项目

摘　　要：以小振幅波理论为基础,利用摄动方法研究了两层密度成层状态下的毛细重力波,求得了两层密度成层状态下各层流体速度势的三阶解及毛细重力波波面位移的三阶Stokes波解.结果表明:三阶方程的解均受到表面张力的影响.三阶Stokes波解描述了毛细重力波的三阶非线性修正,波速不仅取决于波数和各层流体的厚度,而且还与波幅及表面张力有关.The gravity-capillary water Waves in two-layer density-stratified fluid are inves- tigated by using a singular perturbation method, and tile third-order asymptotic solutions of the velocity potentials a^d the third-order Stokes wave solutions of the associated eleva- tions of the interracial waves are presented based on the small amplitude wave theory. As expected, the third-order solutions describe the third-order 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.

关 键 词：两层密度分层流体 毛细重力波 三阶Stokes波解 小振幅波理论 

分 类 号：O353.2[理学—流体力学]