The theory of three-layer density-stratified ideal fluids is examined with a view toward 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 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 Viríssimo and Milewski are also discussed.

Camassa, R., Falqui, G., Ortenzi, G., Pedroni, M., Ho, T. (2021). Hamiltonian Aspects of Three-Layer Stratified Fluids. JOURNAL OF NONLINEAR SCIENCE, 31(4) [10.1007/s00332-021-09726-0].

Hamiltonian Aspects of Three-Layer Stratified Fluids

Falqui, G;Ortenzi, G
;
Pedroni, M;Ho, TTV
2021

Abstract

The theory of three-layer density-stratified ideal fluids is examined with a view toward 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 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 Viríssimo and Milewski are also discussed.
Articolo in rivista - Articolo scientifico
Conservation laws; Hamiltonian PDEs; Long wave models; Mixed type evolution equations; Poisson reductions; Stratified fluids;
English
2021
31
4
70
open
Camassa, R., Falqui, G., Ortenzi, G., Pedroni, M., Ho, T. (2021). Hamiltonian Aspects of Three-Layer Stratified Fluids. JOURNAL OF NONLINEAR SCIENCE, 31(4) [10.1007/s00332-021-09726-0].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/318998
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