旋转重力毛细管双层流中的小振幅孤立界面行波

Small-Amplitude Solitary Interfacial Traveling Waves in a Gravity-Capillary Two-Layered Fluid with Vorticity

该文考虑深度有限,上下边界均固定且受重力及内界面张力作用的二维旋转双层流体.在两层中流体粒子的速度均不超过波速的假设下,证明在该双层流体内部界面上行进的小振幅孤波的存在性.论证过程主要基于中心流形约化定理及动力系统方法.通过考察由原水动力问题所得的哈密尔顿系统在平衡点处线性部分的谱,及其在参数平面内的分叉图,得到了约化方程组的同宿轨道解,这进而给出了内界面上的稳定孤波.

Considered in this paper is a two-dimensional rotational two-layered fluid with finite thickness,rigid bottom and upper lid,and acted upon by gravity and interfacial tension.Under the assumption that in both layers of the fluid the horizontal velocity of the fluid particle does not exceed the wave speed,we prove the existence of small-amplitude solitary waves traveling at the interface of the fluid.The argument is mainly based on the center-manifold reduction technique and the dynamical systems methods.By studying the spectrum of the linearization at the equilibrium of the Hamiltonian system formulated from the hydrodynamic problem,and its bifurcation diagram in the parameter plane,we obtain the homoclinic solutions of the reduced system which gives the solitary interfacial water waves.