具有基本流动的两层流体界面和表面孤波

SOLITARY WAVES ON A TWO-LAYER FLUID WITH BASIC CURRENTS

本文研究了具有基本流动的两层流体浅水孤波,利用多重尺度摄动方法求得了两流体界面和表面波所满足的KdV方程和相应单孤波解;对所得结果进行了讨论,并将其应用到海洋温跃层和有剪切流动的均匀密度流体两种常见情形。

In this paper, we study the interface and surface solitary waves on a two-layer fluid with basic currents. It is found that there are two modes of solitary waves, i.e., the fast mode and rhe slow mode, they are always governed by a KdV equation. The influence of currents on solitary waves is discussed. By using the two-fluid model, the themocline in ocean is studied, the long, weak nonlinear waves in a homogeneous density fluid with shear flow are studied also.