Large mode-2 internal solitary waves in three-layer flows

Abstract

In this paper, we investigate mode-2 solitary waves in a three-layer stratified flow model. Travelling wave solutions to both the fully nonlinear problem (Euler equations), and a three-layer extension of the strongly nonlinear two-layer Miyata-Choi-Camassa equations are found numerically. Mode-2 solitary waves with speeds slower than the linear mode-1 long-wave speed are typically expected to be generalised solitary waves: that is, their tails consist of a resonant modeone 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 exceed the mode-1 linear long wave speed. Further, we show how some forms of the embedded solitary waves are intimately linked to the conjugate states of the problem.