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The slow equations
Author(s) -
Lynch Peter
Publication year - 1989
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.49711548510
Subject(s) - spurious relationship , primitive equations , barotropic fluid , initialization , shallow water equations , physics , independent equation , mathematical analysis , potential vorticity , jump , mathematics , vorticity , simultaneous equations , mechanics , differential equation , computer science , vortex , statistics , quantum mechanics , programming language
A filtered system of equations is derived, using the ideas of normal mode initialization. This slow equation system models the low frequency rotational atmospheric motions; there are no solutions corresponding to gravity waves. The prognostic element of the system is an equation expressing the conservation of potential vorticity. The slow equations differ from the general balance system at second order in the Rossby number, and are free from the spurious solutions found in that system. Integration of a barotropic model with the slow equations shows them to be highly accurate when compared with the primitive equations. Since the slow equation model has no high frequency solutions and is free from data shock, it may be useful for continuous assimilation of observational data.