有流存在下两层密度分层流体毛细重力波的三阶Stokes波解  

Third-Order Stokes Wave Solutions for Gravity-Capillary Waves in Two-Layer Stratified Fluid with Background Current

作　　者：崔巍[1] 木仁[1,2] 陈小刚[1] 沈玉艳[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》2012年第8期159-167,共9页Mathematics in Practice and Theory

基　　金：内蒙古工业大学科研计划项目(ZD201034);内蒙古自治区自然科学基金项目(2011MS1002);内蒙古大学“211工程”创新人才培养项目资助

摘　　要：以小振幅波理论为基础,利用奇异摄动方法研究了有背景流存在下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,并讨论了毛细重力波的kelvin-Helmholtz的不稳定性.结果表明在有流存在的情况下,两层密度成层流体毛细重力波的一阶渐近解、频散关系,二阶渐近解及三阶渐近解不仅依赖于各层流体的厚度和密度,也依赖于表面张力和各层流体的背景流流场;毛细重力波的三阶解描述了背景流场与毛细重力波之问的三阶非线性相互作用.对于给定的波数k(实数)毛细重力波可能出现kelvin-Helmholtz不稳定性.In this paper,gravity-capillary Waves in two-layer stratified fluid with background current are investigated using a singular perturbation method,and the third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the gravity-capillary Waves are presented based on the small amplitude wave theory,and the Kelvin-Helmholtz instability of the interfacial waves is studied.As expected,for two-layer stratified fluid with background current,the first-order asymptotic solutions,dispersion relation,second-order asymptotic solutions and third-order asymptotic solutions derived depend on not only the depths and densities of the two-layer fluid but also the surface tension and the background current of the fluid,and the third-order Stokes wave solutions of the associated elevations of the interfacial waves describe the third-order nonlinear interactions between the gravity-capillary Waves and current.It also shows that with the given wave number k（real number） the gravity-capillary Waves may show Kelvin-Helmholtz instability.

关 键 词：毛细重力波 均匀流 三阶Stokes波解 KELVIN-HELMHOLTZ不稳定性 

分 类 号：O353.2[理学—流体力学]