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Covariant equations for geophysical fluids with an asymmetric gravitational potential and their hydrostatic limit
Author(s) -
Charron Martin,
Zadra Ayrton
Publication year - 2014
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.2435
Subject(s) - hydrostatic equilibrium , tensor (intrinsic definition) , physics , covariant transformation , limit (mathematics) , classical mechanics , consistency (knowledge bases) , gravitation , covariance and contravariance of vectors , mathematical physics , mathematical analysis , mathematics , geometry , quantum mechanics
Starting from the governing equations in tensor form for non‐hydrostatic fluid dynamics, the hydrostatic limit is obtained by introducing a scaling parameter. This allows the use of the same fundamental tensor equations to describe the dynamics of non‐hydrostatic and hydrostatic geophysical fluids, possibly combined with geometric approximations, while preserving the dynamical consistency of the governing equations in arbitrary coordinates. This provides the tools to reproduce in a systematic manner the quartet of equations—deep/non‐hydrostatic, deep/hydrostatic, shallow/non‐hydrostatic, and shallow/hydrostatic—presented elsewhere. This quartet is generalised to the case where the gravitational potential has no spatial symmetries.