2003
DOI: 10.1017/s0022112003005536
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A new family of uniform vortices related to vortex configurations before merging

Abstract: Stimulated by experimental observations of vortex merging, we compute a new family of uniform-vorticity steady solutions of the Euler equations in two dimensions. In experiments with two co-rotating vortices, one finds that, prior to the convective merging phase, and the formation of vortex filaments, the initial pair diffuses into a single structure (with two vorticity peaks) in the form of a symmetric ‘dumb-bell’. In the present computations, our exploration of the existence of vortex solutions has been guid… Show more

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Cited by 32 publications
(25 citation statements)
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“…By procedures such as ͑i͒ the desingularization of point vortices to uniform vortex patches ͑or vice versa͒, ͑ii͒ the growing of new point vortices at corotation points of existing equilibria as done recently by Aref and Vainchtein, 6 ͑iii͒ the growing of new vortex patches at corotation points of existing equilibria as done here, and ͑iv͒ the smooth continuation of touching vortex patches to a merged equilibrium as done here and recently by Cerretelli and Williamson, 17 it appears that even basic equilibria with simple vorticity distributions can be continuously continued to more complicated ones with more elaborate vortical topology.…”
Section: Discussionmentioning
confidence: 89%
“…By procedures such as ͑i͒ the desingularization of point vortices to uniform vortex patches ͑or vice versa͒, ͑ii͒ the growing of new point vortices at corotation points of existing equilibria as done recently by Aref and Vainchtein, 6 ͑iii͒ the growing of new vortex patches at corotation points of existing equilibria as done here, and ͑iv͒ the smooth continuation of touching vortex patches to a merged equilibrium as done here and recently by Cerretelli and Williamson, 17 it appears that even basic equilibria with simple vorticity distributions can be continuously continued to more complicated ones with more elaborate vortical topology.…”
Section: Discussionmentioning
confidence: 89%
“…More recently, the same approach has been extended in an inviscid context to various nonuniform vorticity profiles [26,4] or else to uniform vorticity region which is not formed of two disconnected domains i.e. a dumb-bell shape patch [7]. This latter approach recovers the limiting V-states obtained in [27].…”
Section: Introductionmentioning
confidence: 78%
“…1(a) with a vortex ring surrounding the two vortices. It is also reminiscent of the model solution devised in [7]. Implementing the above ansatz in the vorticity equation, it is readily seen that in the co-rotating frame, the term u · ∇ω scales in Reynolds number like the viscous term ω/Re.…”
Section: The Merging Onsetmentioning
confidence: 97%
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