论文标题
三层流中的大模式-2内部孤立波
Large mode-2 internal solitary waves in three-layer flows
论文作者
论文摘要
在本文中，我们研究了三层分层流模型中模式2孤立波。在数值上发现并比较了三层MIYATA-CHOI-CAMASSA方程的完全非线性问题（Euler方程）和三层MIYATA-CHOI-CAMASSA方程的局部行驶波解。模式2的速度比线性模式-1长波速度慢的单生波通常是通用的孤立波，其无限尾巴由一个由一个谐振模式的周期性波动序列组成。本文我们证明了模式2嵌入式孤立波的存在，也就是说，我们表明，对于参数的特定值，尾部振荡的幅度为零。对于足够厚的中层层，我们还发现模式2孤立波的分支，其速度超出了模式1线性波，并且不再嵌入。此外，我们还展示了嵌入式孤立波的大幅度与问题的共轭状态密切相关。
In this paper, we investigate mode-2 solitary waves in a three-layer stratified flow model. Localised travelling wave solutions to both the fully nonlinear problem (Euler equations), and the three-layer Miyata-Choi-Camassa equations are found numerically and compared. Mode-2 solitary waves with speeds slower than the linear mode-1 long-wave speed are typically generalised solitary waves with infinite tails consisting of a resonant mode-one periodic wave train. Herein we evidence the existence of mode-2 embedded solitary waves, that is, we show that for specific values of the parameters, the amplitude of the oscillations in the tail are zero. For sufficiently thick middle layers, we also find branches of mode-2 solitary waves with speeds that extend beyond the mode-1 linear waves and are no longer embedded. In addition, we show how large amplitude embedded solitary waves are intimately linked to the conjugate states of the problem.
