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以小振幅波理论为基础,利用摄动方法研究了有背景流场存在时密度三层成层状态下的界面内波,得到了各层流体速度势的二阶渐近解及界面内波波面位移的二阶Stokes波解,并讨论了界面波的Kelvin-Helmholtz不稳定性.结果表明:有流存在的情况下三层密度成层流体界面内波的一阶渐近解(线性波解)、频散关系及二阶渐近解不仅依赖于各层流体的厚度和密度,也依赖于各层流体的背景流场;界面内波波面位移的二阶Stokes波解不仅描述了界面波之间的二阶非线性相互作用,也描述了背景流与界面波之间的二阶非线性相互作用;当每层流体的水平流速均为零时,所得到的渐近解是一个特例;对于给定的波数k(实数),界面波可能会出现Kelvin-Helmholtz不稳定性.
Based on the theory of small amplitude waves, the interfacial interfacial waves under three layers delamination in the presence of the background flow field are studied by the perturbation method. The second order asymptotic solutions of the fluid velocity potentials and the inner wave surface Order Stokes wave and the Kelvin-Helmholtz instability of the interface wave is discussed.The results show that the first-order asymptotic solution (linear wave solution) of the inner wave in the interface of the three- , The dispersion relationship and the second-order asymptotic solution depend not only on the thickness and density of the fluid in each layer, but also on the background flow field of the fluid in each layer. The second-order Stokes wave solutions of the wave surface displacements in the interface not only describe the inter- The second-order nonlinear interaction between the background and the interface wave is also described. The asymptotic solution obtained when the horizontal velocity of each fluid is zero is a special case. Given the wave number k (real number), the interface wave may exhibit Kelvin-Helmholtz instability.