Simulation of Internal Undular Bores in Rapidly Varying Topography

Abstract

This paper intends to look at the influence of rapidly varying regions on the propagation of internal undular bores in a two-layer fluid flow. Internal undular bores have been observed in the ocean around the world. The appropriate mathematical model to describe the evolution of internal undular bores in a stratified fluid is the variable-coefficient extended Korteweg-de Vries equation. The governing equation is solved numerically using the method of lines to simulate the propagation of internal undular bores. Our numerical results show that the effects of rapidly varying topography lead to adiabatic and non-adiabatic deformation of the internal undular bores, including the generation of solitary wavetrain, generation of nonlinear wavetrain and generation of rarefaction wave. Besides, multi-phase behaviour is also observed during the evolution.