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Abstract
We examine the form, properties, stability and evolution of doublyconnected (twovortex) relative equilibria in the singlelayer ƒplane quasigeostrophic shallowwater model of geophysical fluid dynamics. Three parameters completely describe families of equilibria in this system: the ratio γ =L/L_{D }between the horizontal size of the vortices and the Rossby deformation length; the area ratio α of the smaller to the larger vortex; and the minimum distance δ between the two vortices. We vary 0 < γ ≤ 10 and 0.1 ≤ α ≤ 1.0, determining the boundary of stability δ = δ_{C}(γ,α). We also examine the nonlinear development of the instabilities and the transitions to other nearequilibrium configurations. Two modes of instability occur when δ < δ_{C}: a small γ asymmetric (wave 3) mode, which is absent for α ≳ 0.6; and a large γ mode. In general, major structural changes take place during the nonlinear evolution of the vortices, which near δ_{C }may be classified as follows: (i) vacillations about equilibrium for γ ≳ 2.5; (ii) partial straining out, associated with the small γ mode, where either one or both of the vortices get smaller for γ ≲ 2.5 and α ≲ 0.6; (iii) partial merger, occurring at the transition region between the two modes of instability, where one of the vortices gets bigger, and (iv) complete merger, associated with the largeγ mode. We also find that although conservative inviscid transitions to equilibria with the same energy, angular momentum and circulation are possible, they are not the preferred evolutionary path.
Original language  English 

Pages (fromto)  4068 
Number of pages  29 
Journal  Journal of Fluid Mechanics 
Volume  723 
Early online date  16 Apr 2013 
DOIs  
Publication status  Published  May 2013 
Keywords
 Contour dynamics
 Rotating flows
 Vortex dynamics
 Vstates
 2dimensional vortex
 Uniform vortices
 2 dimensions
 Numerical algorithms
 Coherent structures
 Euler equations
 Merger
 Flows
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Dive into the research topics of 'Quasigeostrophic shallowwater doublyconnected vortex equilibria and their stability'. Together they form a unique fingerprint.Projects
 1 Finished

Geophysical Vortices: The Structure, stability and interaction of geophysical vortices
Reinaud, J. N., Dritschel, D. G. & Scott, R. K.
5/01/10 → 1/11/13
Project: Standard