Dynamics of Strongly Nonlinear Internal Solitary Waves in Shallow Water

Abstract

We study the dynamics of large amplitude internal solitary waves in shallow water by using a strongly nonlinear long‐wave model. We investigate higher order nonlinear effects on the evolution of solitary waves by comparing our numerical solutions of the model with weakly nonlinear solutions. We carry out the local stability analysis of solitary wave solution of the model and identify an instability mechanism of the Kelvin–Helmholtz type. With parameters in the stable range, we simulate the interaction of two solitary waves: both head‐on and overtaking collisions. We also study the deformation of a solitary wave propagating over non‐uniform topography and describe the process of disintegration in detail. Our numerical solutions unveil new dynamical behaviors of large amplitude internal solitary waves, to which any weakly nonlinear model is inapplicable.