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

2024/11/15 by Roberto Camassa, G. Falqui, Camassa, R. +7
Engineering · Mathematics · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Geophysics (physics.geo-ph) #Lattice Boltzmann Simulation Studies #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2411.15171

openalex publication_date 2024/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

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.

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