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Semi‐geostrophic time evolution of velocity gradient tensor invariants
Author(s) -
Roulstone I.,
White A. A.
Publication year - 2016
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.2841
Subject(s) - baroclinity , geostrophic wind , potential vorticity , jacobian matrix and determinant , balanced flow , classical mechanics , hydrostatic equilibrium , mathematics , vorticity , mathematical analysis , flow (mathematics) , physics , mechanics , geometry , vortex , quantum mechanics
The behaviour of quadratic invariants of the velocity gradient tensor is explored when the time evolution is governed by semi‐geostrophic forms of the shallow‐water equations. The evolution equation of a certain Jacobian involving the geostrophic flow is formally similar to its counterpart under the primitive shallow‐water equations. The resultant deformation and the Frobenius norm do not behave in this symmetrical way. A product of the study is a straightforward derivation of the semi‐geostrophic potential vorticity conservation property. Results are extended to 3D baroclinic flow by using isentropic coordinates.