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arXiv · 2105.12851

Hamiltonian aspects of 3-layer stratified fluids

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

The theory of 3-layer density stratified ideal fluids is examined with a view towards its generalization to the n-layer case. The focus is on structural properties, especially for the case of a rigid upper lid constraint. We show that the long-wave dispersionless limit is a system of quasi-linear equations that do not admit Riemann invariants. We equip the layer-averaged one-dimensional model with a natural Hamiltonian structure, obtained with a suitable reduction process from the continuous density stratification structure of the full two-dimensional equations proposed by Benjamin. For a a laterally unbounded fluid between horizontal rigid boundaries, the paradox about the non-conservation of horizontal total momentum is revisited, and it is shown that the pressure imbalances causing it can be intensified by three-layer setups with respect to their two-layer counterparts. The generator of the x-translational symmetry in the n-layer setup is also identified by the appropriate Hamiltonian formalism. The Boussinesq limit and a family of special solutions recently introduced by de Melo Virissimo and Milewski are also discussed.

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R. Camassa, G. Falqui, G. Ortenzi, M. Pedroni, T. T. Vu Ho. 2021-05-26. Hamiltonian aspects of 3-layer stratified fluids. https://doi.org/10.1007/s00332-021-09726-0

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