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Reinaud2002JFluidMech469-Merger.pdf792.27 kBAdobe PDFView/Open
Title: The merger of vertically offset quasi-geostrophic vortices
Authors: Reinaud, Jean Noel
Dritschel, David Gerard
Keywords: Vortex Dynamics
QA Mathematics
Issue Date: 25-Oct-2002
Citation: Reinaud , J N & Dritschel , D G 2002 , ' The merger of vertically offset quasi-geostrophic vortices ' Journal of Fluid Mechanics , vol 469 , pp. 287-315 . , 10.1017/S0022112002001854
Abstract: We examine the critical merging distance between two equal-volume, equal-potential-vorticity quasi-geostrophic vortices. We focus on how this distance depends on the vertical offset between the two vortices, each having a unit mean height-to-width aspect ratio. The vertical direction is special in the quasi-geostrophic model (used to capture the leading-order dynamical features of stably stratified and rapidly rotating geophysical flows) since vertical advection is absent. Nevertheless vortex merger may still occur by horizontal advection. In this paper, we first investigate the equilibrium states for the two vortices as a function of their vertical and horizontal separation. We examine their basic properties together with their linear stability. These findings are next compared to numerical simulations of the nonlinear evolution of two spheres of potential vorticity. Three different regimes of interaction are identified, depending on the vertical offset. For a small offset, the interaction differs little from the case when the two vortices are horizontally aligned. On the other hand, when the vertical offset is comparable to the mean vortex radius, strong interaction occurs for greater horizontal gaps than in the horizontally aligned case, and therefore at significantly greater full separation distances. This perhaps surprising result is consistent with the linear stability analysis and appears to be a consequence of the anisotropy of the quasi-geostrophic equations. Finally, for large vertical offsets, vortex merger results in the formation of a metastable tilted dumbbell vortex.
Version: Publisher PDF
Status: Peer reviewed
ISSN: 0022-1120
Type: Journal article
Rights: (c)2002 Cambridge University Press
Appears in Collections:University of St Andrews Research
Applied Mathematics Research

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