Hamiltonian Aspects of Three-Layer Stratified Fluids
Abstract
The theory of three-layer density-stratified ideal fluids is examined with a view toward its generalization to then-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 thex-translational symmetry in then-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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 16, 2021
- Source ID
- 10.1007/s00332-021-09726-0
Entities
People
- Giovanni Ortenzi
- Gregorio Falqui
- Marco Pedroni
- Roberto Camassa
- T. T. Vu Ho
Organizations
- Marie Skłodowska-Curie Actions
- National Science Foundation
- Office of Naval Research