三层密度分层流体界面波的二阶Stokes波解

Second-order Stokes wave solutions for interfacial waves in three-layer density stratified fluids

借助正则摄动法，利用小振幅波理论，研究上表面为自由表面、下底面为刚性边界的三层密度稳定分层、无旋、无粘、不可压缩流体系统的界面波，即自由表面波和界面内波，给出二维情形下自由表面波及各界面内波的二阶Stokes波解。研究表明：自由表面波及各界面内波的一阶渐近解为线性波解，二阶渐近解由一阶渐近解及自由表面波和各界面内波之间的二阶非线性修正及二阶非线性相互作用确定，所得到的一阶渐近解和二阶渐近解分别与流体系统中各层的密度与厚度有关，波动频散关系是关于ω2的三次多项式，它的解对应于自由表面波及各界面内波的三个运动模态。

With the regular perturbation method, the interfacial waves, which include the free surface wave and the interfacial-internal waves, are discussed by using the small amplitude wave theory in the three-layer density stable stratified fluid system with the free upper boundary and the fiat impermeable bottom in which the fluids are irrotational, inviseid and incompressible. The two-dimensional second-order Stokes wave solutions of the free surface wave and the interfacial-internal waves are given. It is noted that the first-order asymptotic solutions for the free surface wave and the interracial internal waves are linear wave solutions, and the second-order asymptotic solutions are determined by the first-order asymptotic solutions, the second-order nonlinear modification, the second-order nonlinear interactions between the free surface wave and the interracial internal waves. The received first-order asymptotic solutions and the second-order asymptotic solutions are relating to the densities and the depths of each layer fluid. The dispersion relation of interracial waves is a third-order polynomial of ω2 , and its solutions are corresponding to the three-movement modes of the free surface wave and the interracial-internal waves.