三层流体界面内波的二阶Stokes解

以小振幅波理论为基础，利用摄动方法研究了三层密度成层状态下的界面内波，求得了三层成层状态下各层速度势的二阶渐近解及界面内波波面位移的二阶Stokes解.结果表明：一阶解为正弦波解，与传统线性理论的结果相一致；二阶解描述了界面波的二阶非线性修正及两界面波之间的非线性相互作用；一阶解及二阶解都依赖于各层流体的厚度及密度.Umeyama导出的理论结果为本文的特殊情形.关键词：三层密度成层流体内波二阶Stokes解小振幅波理论

Second-order Stokes solutions for internal waves in three-layer density-stratified fluid

In this paper, internal waves in three-layer stratified fluid are investigated by using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. As expected, the first-order solutions are consistent with ordinary linear theoretical results, and the second-order solutions describe the second-order modification on the linear theory and the interactions between the two interfacial waves. Both the first-order and second-order solutions derived depend on the depths and densities of the three-layer fluid. It is also noted that the solutions obtained from the present work include the theoretical results derived by Umeyama as special cases.