A Hamiltonian set-up for 4-layer density stratified Euler fluids

TL;DR

This paper develops a Hamiltonian framework for modeling four-layer density-stratified Euler fluids in a channel, deriving equations of motion in the long-wave limit and exploring symmetric solutions.

Contribution

It introduces a Hamiltonian structure for four-layer stratified fluids and extends previous three-layer models to this more complex configuration.

Findings

Derived Hamiltonian and equations of motion in the Boussinesq approximation.

Identified symmetric solutions generalizing three-layer cases.

Analyzed the existence of special symmetric solutions.

Abstract

By means of the Hamiltonian approach to two-dimensional wave motions in heterogeneous fluids proposed by Benjamin, we derive a natural Hamiltonian structure for ideal fluids, density stratified in four homogenous layers, constrained in a channel of fixed total height and infinite lateral length. We derive the Hamiltonian and the equations of motion in the dispersionless long-wave limit, restricting ourselves to the so-called Boussinesq approximation. The existence of special symmetric solutions, which generalize to the four-layer case the ones obtained in the paper for the three-layer case, is examined.