Wave Vibration and Simulation in Dissipative Media Described by Irregular Boundary Surfaces: A Mathematical Formulation

Abstract

Internal waves are gravity waves that occur within a stratified fluid rather than on the surface. The governing equations are derived to cover density differences in a stratified two-layer fluid within a two-dimensional internal wave domain in this study. The proposed perturbation model considers the relationship between nonlinearity and frequency dispersion at O(\(\varepsilon\)) = O(\(\mu\)²) but ignores the viscous effects. The governing equations are formed based on the continuity equation and Euler equations to simulate the realistic movement of an experimental internal solitary wave (ISW) over a variable seabed. The focus is on using the equations governing interfacial wave motion to describe the motion in detail, especially the interaction between an ISW and the seabed topography.