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contributor authorViúdez, Álvaro
date accessioned2017-06-09T16:52:19Z
date available2017-06-09T16:52:19Z
date copyright2005/07/01
date issued2005
identifier issn0022-4928
identifier otherams-75669.pdf
identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4218030
description abstractA new derivation and interpretation of the semigeostrophic (SG) material invariant in the theory of geophysical flows is introduced. First, a generalized three-dimensional equation of the SG dynamics is established and the generalized equations for the rate of change of vorticity and for the rate of change of the velocity gradient cofactor tensor are obtained. Next, a conservation equation for the vorticity?velocity gradient cofactor tensor (denoted ??) is derived. The specific potential ??, that is, ?? in the reference configuration per unit of mass, is defined and an expression for its rate of change is obtained. The SG invariant is interpreted as the vertical component of the specific potential ??. Under the SG assumptions (advection of the geostrophic velocity, hydrostatic, and f-plane approximations) this vertical component is materially conserved in the SG flow. The generalized SG invariant (i.e., the specific potential ??) differs conceptually from the Beltrami?Rossby?Ertel specific potential vorticity. Its conservation in the SG flow seems to be highly dependent on the SG assumptions, especially on the f-plane approximation and on the horizontal nature of the geostrophic velocity.
publisherAmerican Meteorological Society
titleThe Vorticity–Velocity Gradient Cofactor Tensor and the Material Invariant of the Semigeostrophic Theory
typeJournal Paper
journal volume62
journal issue7
journal titleJournal of the Atmospheric Sciences
identifier doi10.1175/JAS3482.1
journal fristpage2294
journal lastpage2301
treeJournal of the Atmospheric Sciences:;2005:;Volume( 062 ):;issue: 007
contenttypeFulltext


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