Dynamics of strongly nonlinear internal long waves in a three-layer fluid system

Abstract

Dynamics of internal solitary waves in shallow water were studied with a strongly nonlinear internal long wave model in a three-layer fluid system. It is an extension of the two-layer MCC (Miyata, Choi, and Camassa) model, which is derived under the assumption that the characteristic wavelength is long in comparison to the thickness of each fluid layer. Phase velocity was assessed to understand the stability of solitary waves when they propagate. The instability mechanism turns out to be a Kelvin-Helmholtz type instability that is similar to the twolayer MCC model. We numerically investigated the three-layer model in terms of the effects of the middle layer and non-uniform bottom topography, and examined the generation of solitary waves to demonstrate the rich dynamics of the three-layer model.