| Journal: | Revista mexicana de física |
| Database: | PERIÓDICA |
| System number: | 000447135 |
| ISSN: | 0035-001X |
| Authors: | Beron Vera, F.J1 |
| Institutions: | 1University of Miami, School of Marine & Atmospheric Science, Miami, Florida. Estados Unidos de América |
| Year: | 2021 |
| Season: | May-Jun |
| Volumen: | 67 |
| Number: | 3 |
| Pages: | 351-364 |
| Country: | México |
| Language: | Inglés |
| Document type: | Artículo |
| Approach: | Analítico, teórico |
| English abstract | The purpose of this paper is to present a shallow-water-type model with multiple inhomogeneous layers featuring variable linear velocity vertical shear and stratification in horizontal space and time. This is achieved by writing the layer velocity and buoyancy fields as linear functions of depth, with coefficients that depend arbitrarily on horizontal position and time. The model is a generalization of Ripa’s (1995) single-layer model to an arbitrary number of layers. Unlike models with homogeneous layers, the present model can represent thermodynamics processes driven by heat and freshwater fluxes through the surface or mixing processes resulting from fluid exchanges across contiguous layers. By contrast with inhomogeneous-layer models with depth-independent velocity and buoyancy, the model derived here can sustain explicitly at a low frequency a current in thermal wind balance (between the vertical vertical shear and the horizontal density gradient) within each layer. In the absence of external forcing and dissipation, energy, volume, mass, and buoyancy variance constrain the dynamics; conservation of total zonal momentum requires also the usual zonal symmetry of the topography and horizontal domain. The inviscid, unforced model admits a formulation suggestive of a generalized Hamiltonian structure, which enables the classical connection between symmetries and conservation laws via Noether’s theorem. A steady solution to a system involving one Ripa-like layer and otherwise homogeneous layers can be proved formally (or Arnold) stable using the above invariants. A model configuration with only one layer has been previously shown to provide: a very good representation of the exact vertical normal modes up to the first internal mode; an exact representation of long-perturbation (free boundary) baroclinic instability; and a very reasonable representation of short-perturbation (classical Eady) baroclinic instability. Here it is shown that substantially mo |
| Disciplines: | Física y astronomía |
| Keyword: | Termodinámica y física estadística, Ecuaciones de aguas poco profundas, Capas no homogéneas, Estratificación, Cizallamiento |
| Keyword: | Thermodynamics and statistical physics, Shallow water equations, Inhomogeneous layers, Stratification, Shear |
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