dorsal/arxiv
View SchemaMultilayer shallow-water model with stratification and shear
| Authors | F. J. Beron-Vera |
|---|---|
| Categories | |
| ArXiv ID | physics/0312083 |
| URL | https://arxiv.org/abs/physics/0312083 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
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 startificaion 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 is able to represent thermodynamics processes driven by heat and freshwater fluxes through the surface or mixing processes resulting from fluid exchanges across contiguous layers. 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 more accurate overall results with respect to single-layer calculations can be achieved by considering a stack of only a few layers. A similar behavior is found in ageostrophic (classical Stone) baroclinic instability by describing accurately the dependence of the solutions on the Richardson number with only two layers.
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"date_created": "2026-03-02T18:00:46.034000Z",
"date_modified": "2026-03-02T18:00:46.034000Z",
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"abstract": "The purpose of this paper is to present a shallow-water-type model with\nmultiple inhomogeneous layers featuring variable linear velocity vertical shear\nand startificaion in horizontal space and time. This is achieved by writing the\nlayer velocity and buoyancy fields as linear functions of depth, with\ncoefficients that depend arbitrarily on horizontal position and time. The model\nis a generalization of Ripa\u0027s (1995) single-layer model to an arbitrary number\nof layers. Unlike models with homogeneous layers the present model is able to\nrepresent thermodynamics processes driven by heat and freshwater fluxes through\nthe surface or mixing processes resulting from fluid exchanges across\ncontiguous layers. A model configuration with only one layer has been\npreviously shown to provide: a very good representation of the exact vertical\nnormal modes up to the first internal mode; an exact representation of\nlong-perturbation (free boundary) baroclinic instability; and a very reasonable\nrepresentation of short-perturbation (classical Eady) baroclinic instability.\nHere it is shown that substantially more accurate overall results with respect\nto single-layer calculations can be achieved by considering a stack of only a\nfew layers. A similar behavior is found in ageostrophic (classical Stone)\nbaroclinic instability by describing accurately the dependence of the solutions\non the Richardson number with only two layers.",
"arxiv_id": "physics/0312083",
"authors": [
"F. J. Beron-Vera"
],
"categories": [
"physics.ao-ph"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Multilayer shallow-water model with stratification and shear",
"url": "https://arxiv.org/abs/physics/0312083"
},
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