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A merging criterion for two-dimensional co-rotating vortices

Abstract : We propose a quantitative criterion for the merging of a pair of equal two-dimensional co-rotating vortices. A cross-validation between experimental and theoretical analyses is performed. Experimental vortices are generated by the roll-up of a vortex sheet originating from the identical and impulsive rotation of two plates. The phenomenon is then followed up in time until a rapid pairing transition occurs for which critical parameters are measured. In the theoretical approach, the nonlinear Euler solution representing a pair of equal vortices is computed for various nonuniform vorticity distributions. The stability analysis of such a configuration then provides critical values for the onset of merging. From this data set, a criterion depending on global impulse quantities is extracted for different shapes of the vorticity distribution. This theoretical statement agrees well with our experimentally based criterion.
Mots-clés : vortex fusion
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Patrice Meunier, Uwe Ehrenstein, Thomas Leweke, Maurice Rossi. A merging criterion for two-dimensional co-rotating vortices. Physics of Fluids, American Institute of Physics, 2002, 14, n° 8, pp.2757-2766. ⟨10.1063/1.1489683⟩. ⟨hal-00081683⟩

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