The Dynamics of Flat Surface Internal Geophysical Waves with Currents

TL;DR

This paper models the dynamics of internal geophysical waves with currents in a two-layer fluid system, deriving Hamiltonian formulations, analyzing limiting behaviors, and providing linear and long-wave approximations.

Contribution

It introduces a Hamiltonian framework for internal waves with depth-dependent currents, extending previous models and analyzing their limiting behaviors.

Findings

Hamiltonian formulation of internal wave system

Comparison of limiting behaviors with existing models

Derivation of linear and long-wave approximations

Abstract

A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or thermocline in the ocean. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. A current profile with depth-dependent currents in each domain is considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behaviour is examined and compared to that of other known models. The linearised equations as well as long-wave approximations are presented.