dorsal/arxiv
View SchemaConstrained-Hamiltonian Shallow-Water Dynamics on the Sphere
| Authors | F. J. Beron-Vera |
|---|---|
| Categories | |
| ArXiv ID | physics/0307141 |
| URL | https://arxiv.org/abs/physics/0307141 |
Abstract
Salmon's nearly geostrophic model for rotating shallow-water flow is derived in full spherical geometry. The model, which results upon constraining the velocity field to the height field in Hamilton's principle for rotating shallow-water dynamics, constitutes an important prototype of Hamiltonian balanced models. Instead of Salmon's original approach, which consists in taking variations of particle paths at fixed Lagrangian labels and time, Holm's approach is considered here, namely variations are taken on Lagrangian particle labels at fixed Eulerian positions and time. Unlike the classical quasigeostrophic model, Salmon's is found to be sensitive to the differences between geographic and geodesic coordinates. One consequence of this result is that the $\beta $ plane approximation, which is included in Salmon's original derivation, is not consistent for this class of model.
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"abstract": "Salmon\u0027s nearly geostrophic model for rotating shallow-water flow is derived\nin full spherical geometry. The model, which results upon constraining the\nvelocity field to the height field in Hamilton\u0027s principle for rotating\nshallow-water dynamics, constitutes an important prototype of Hamiltonian\nbalanced models. Instead of Salmon\u0027s original approach, which consists in\ntaking variations of particle paths at fixed Lagrangian labels and time, Holm\u0027s\napproach is considered here, namely variations are taken on Lagrangian particle\nlabels at fixed Eulerian positions and time. Unlike the classical\nquasigeostrophic model, Salmon\u0027s is found to be sensitive to the differences\nbetween geographic and geodesic coordinates. One consequence of this result is\nthat the $\\beta $ plane approximation, which is included in Salmon\u0027s original\nderivation, is not consistent for this class of model.",
"arxiv_id": "physics/0307141",
"authors": [
"F. J. Beron-Vera"
],
"categories": [
"physics.ao-ph"
],
"title": "Constrained-Hamiltonian Shallow-Water Dynamics on the Sphere",
"url": "https://arxiv.org/abs/physics/0307141"
},
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"execution_id": "f8fd4c3d-d6c2-4f12-80ea-948517f3274e",
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