Euler描述下三层密度分层流体界面内波的二阶驻波解

The Second-order Eulerian Standing Wave Solutions for Nterfacial IInternal Waves in Three-layer Density-stratified Fluids

本文借助摄动展开法,以小振幅波理论为基础,研究了Euler描述下上底面及下底面均为刚性边界的三层密度分层的无旋、无粘、不可压缩流体的界面波,分别求得各层流体速度势的二阶近似解及各界面内波波面位移的二阶驻波解.结果表明:界面波一阶近似解为线性波解,二阶近似解是由一阶近似解及界面内波间二阶非线性修正和二阶非线性的相互作用来确定,一阶解及二阶解均依赖于分层流体的厚度和密度.

In this paper,based on the small amplitude wave theory,the Eulerian interfacial-internal waves in three-layer density-stratified fluids are investigated by using aperturbation method,where the fluids are irrotational,inviscid and incompressible,and the upper boundary and the bottom are rigid boundary.The second-order asymptotic solutions of the velocity potentials and the second-order standing wave solutions of the associated elevations of the interfacial-internal waves are found respectively.The result shows that the first-order asymptotic solutions of the the interfacial-internal waves are linear wave solutions,and the second-order asymptotic solutions are determined by the first-order solutions,the second-order nonlinear modification and the second-order nonlinear interactions between the interfacial waves.Both the first-order and second-order solutions depend on depth and densities of the stratifiedr fluids.