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DritschelReinaudMcKiver2004-JFluidMech505-Quasi-geostrophic.pdf286.89 kBAdobe PDFView/Open
Title: The quasi-geostrophic ellipsoidal vortex model
Authors: Dritschel, David Gerard
Reinaud, Jean Noel
McKiver, William J
Keywords: Stratified fluid
Elliptic model
Vortices
Shear
Equations
Flows
Dynamics
Merger
Motion
QA Mathematics
Issue Date: 25-Apr-2004
Citation: Dritschel , D G , Reinaud , J N & McKiver , W J 2004 , ' The quasi-geostrophic ellipsoidal vortex model ' Journal of Fluid Mechanics , vol 505 , pp. 201-223 .
Abstract: We present a simple approximate model for studying general aspects of vortex interactions in a rotating stably-stratified fluid. The model idealizes vortices by ellipsoidal volumes of uniform potential vorticity, a materially conserved quantity in an inviscid, adiabatic fluid. Each vortex thus possesses 9 degrees of freedom, 3 for the centroid and 6 for the shape and orientation. Here, we develop equations for the time evolution of these quantities for a general system of interacting vortices. An isolated ellipsoidal vortex is well known to remain ellipsoidal in a fluid with constant background rotation and uniform stratification, as considered here. However, the interaction between any two ellipsoids in general induces weak non-ellipsoidal perturbations. We develop a unique projection method, which follows directly from the Hamiltonian structure of the system, that effectively retains just the part of the interaction which preserves ellipsoidal shapes. This method does not use a moment expansion, e.g. local expansions of the flow in a Taylor series. It is in fact more general, and consequently more accurate. Comparisons of the new model with the full equations of motion prove remarkably close.
Version: Publisher PDF
Status: Peer reviewed
URI: http://hdl.handle.net/10023/1556
DOI: http://dx.doi.org/10.1017/S0022112004008377
ISSN: 0022-1120
Type: Journal article
Rights: (c) 2004 Cambridge University Press
Appears in Collections:University of St Andrews Research
Applied Mathematics Research



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