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A concise derivation of the semi‐geostrophic equations
Author(s) -
Chynoweth S.,
Sewell M. J.
Publication year - 1991
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.49711750202
Subject(s) - mathematics , jacobian matrix and determinant , geostrophic wind , curvature , legendre polynomials , mathematical analysis , expression (computer science) , derivative (finance) , front (military) , physics , geometry , meteorology , computer science , mechanics , financial economics , economics , programming language
A self‐contained account of the semi‐geostrophic equations is given. This contains formulae not previously available in the literature. The equations are presented in terms of four alternative sets of independent variables, and the Legendre mappings between these variables are specified. The approach is facilitated by the introduction of a general theorem in vector analysis, which is proved, concerning the total or convected derivative of a Jacobian following the particle. An expression for the curvature of a front is included.