Hamiltonian approach to modelling interfacial internal waves over variable bottom

TL;DR

This paper develops a Hamiltonian framework to model internal waves over uneven bottoms, incorporating effects like vorticity, Coriolis force, and variable bathymetry, with applications to equatorial internal waves and soliton dynamics.

Contribution

It introduces a Hamiltonian model for internal waves that accounts for variable bottom topography, vorticity, and geophysical effects, extending previous models to more realistic oceanic conditions.

Findings

Derivation of a KdV-mKdV type equation with variable coefficients for the interface.

Numerical analysis of soliton fission over variable depth.

Insights into wave-current interactions and effects of bathymetry on internal wave propagation.

Abstract

We study the effects of an uneven bottom on the internal wave propagation in the presence of stratification and underlying non-uniform currents. Thus, the presented models incorporate vorticity (wave-current interactions), geophysical effects (Coriolis force) and a variable bathymetry. An example of the physical situation described above is well illustrated by the equatorial internal waves in the presence of the Equatorial Undercurrent (EUC). We find that the interface (physically coinciding with the thermocline and the pycnocline) satisfies in the long wave approximation a KdV-mKdV type equation with variable coefficients. The soliton propagation over variable depth leads to effects such as soliton fission, which is analysed and studied numerically as well.