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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.
Based on the theory of small amplitude wave, the interfacial interfacial waves under three levels of density stratification were studied by perturbation method. The second order asymptotic solutions of the velocity potentials and the wave surface displacements in the interface The results show that the first order solution is a sine wave solution, which is consistent with the traditional linear theory. The second order solution describes the second order nonlinear modification of interface wave and the nonlinear interaction between two interface waves. The first-order solution and the second-order solution depend on the thickness and density of fluids in each layer. The theoretical result derived by Umeyama is a special case of this paper.