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Dynamically consistent shallow‐atmosphere equations with a complete Coriolis force
Author(s) -
Tort M.,
Dubos T.
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.2274
Subject(s) - hydrostatic equilibrium , primitive equations , atmosphere (unit) , angular momentum , physics , potential vorticity , classical mechanics , momentum (technical analysis) , vorticity , earth's rotation , rotation (mathematics) , action (physics) , mechanics , lagrangian , shallow water equations , mathematics , vortex , geometry , meteorology , partial differential equation , mathematical physics , finance , economics , quantum mechanics , numerical partial differential equations
Shallow‐atmosphere equations retaining both the vertical and horizontal components of the Coriolis force (the latter being neglected in the traditional approximation) are obtained. The derivation invokes Hamilton's principle of least action with an approximate Lagrangian capturing the small increase with height of the solid‐body velocity due to planetary rotation. The conservation of energy, angular momentum and Ertel's potential vorticity are ensured in both quasi‐ and non‐hydrostatic systems.