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Exact axisymmetric solutions of the deep‐ and shallow‐atmosphere Euler equations in curvilinear and plane geometries
Author(s) -
Staniforth Andrew,
Wood Nigel
Publication year - 2012
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.2018
Subject(s) - curvilinear coordinates , atmosphere (unit) , euler equations , baroclinity , plane (geometry) , euler's formula , rotational symmetry , mathematics , mathematical analysis , geometry , physics , mechanics , meteorology
A wide family of exact closed‐form axisymmetric solutions to the deep‐ and shallow‐atmosphere Euler equations is derived. These solutions are not only valid in general curvilinear geometry, but also in beta‐plane and beta–gamma‐plane geometries. A further generalisation of the generalised thermal wind equation is also derived. The enhanced generality of the exact solutions developed herein provides more flexibility in the specification of initial conditions for numerical model validation. This permits the construction not only of more challenging, balanced, shallow‐ and deep‐atmosphere solutions than has hitherto been possible, but also of more elaborate tests of the baroclinic wave type. Copyright © 2012 British Crown copyright, the Met Office. Published by John Wiley & Sons Ltd.