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ReinaudDritschel2005-JFluidMech522-Critical.pdf1.11 MBAdobe PDFView/Open
Title: The critical merger distance between two co-rotating quasi-geostrophic vortices
Authors: Reinaud, Jean Noel
Dritschel, David Gerard
Keywords: Ellipsoidal vortex model
Stratified fluid
QA Mathematics
Issue Date: 10-Jan-2005
Citation: Reinaud , J N & Dritschel , D G 2005 , ' The critical merger distance between two co-rotating quasi-geostrophic vortices ' Journal of Fluid Mechanics , vol 522 , pp. 357-381 . , 10.1017/S0022112004002022
Abstract: This paper examines the critical merger or strong interaction distance between two equal-potential-vorticity quasi-geostrophic vortices. The interaction between the two vortices depends on five parameters: their volume ratio, their height-to-width aspect ratios and their vertical and horizontal offsets. Due to the size of the parameter space, a direct investigation solving the full quasi-geostrophic equations is impossible. We instead determine the critical merger distance approximately using an asymptotic approach. We associate the merger distance with the margin of stability for a family of equilibrium states having prescribed aspect and volume ratios, and vertical offset. The equilibrium states are obtained using an asymptotic solution method which models vortices by ellipsoids. The margin itself is determined by a linear stability analysis. We focus on the interaction between oblate to moderately prolate vortices, the shapes most commonly found in turbulence. Here, a new unexpected instability is found and discussed for prolate vortices which is manifested by the tilting of vortices toward each other. It implies than tall vortices may merge starting from greater separation distances than previously thought.
Version: Publisher PDF
Status: Peer reviewed
ISSN: 0022-1120
Type: Journal article
Rights: (c)2005 Cambridge University Press
Appears in Collections:University of St Andrews Research
Applied Mathematics Research

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