A merging criterion for two-dimensional co-rotating vortices

Patrice Meunier (1) , Uwe Ehrenstein (2) , Thomas Leweke (1) , Maurice Rossi (3)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre
2 JAD - Laboratoire Jean Alexandre Dieudonné
3 LMM - Laboratoire de modélisation en mécanique

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

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Patrice Meunier, Uwe Ehrenstein, Thomas Leweke, Maurice Rossi. A merging criterion for two-dimensional co-rotating vortices. Physics of Fluids, 2002, 14, n° 8, pp.2757-2766. ⟨10.1063/1.1489683⟩. ⟨hal-00081683⟩