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

R. Camassa; G. Falqui; G. Ortenzi; M. Pedroni; T. T. Vu Ho

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arXiv · 2411.15171

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

R. Camassa·G. Falqui·G. Ortenzi·M. Pedroni·T. T. Vu Ho

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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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R. Camassa, G. Falqui, G. Ortenzi, M. Pedroni, T. T. Vu Ho. 2024-11-15. A Hamiltonian set-up for 4-layer density stratified Euler fluids. https://arxiv.org/abs/2411.15171

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