Theoretical analysis of the zigzag instability of a vertical co-rotating vortex pair in a strongly stratified fluid

Pantxika Otheguy (1, 2) , Paul Billant (1) , Jean-Marc Chomaz (1)

1 LadHyX - Laboratoire d'hydrodynamique
2 Centre Technique Littoral, Lyonnaise des Eaux, Technopole Izarbel, Pavillon Izarbel, 64210 Bidart, France

A long-wavelength stability analysis of two co-rotating Gaussian vertical vortices in an inviscid strongly stratified fluid is conducted for vortices separated by a large distance b compared to their radius a (b > a). This analysis predicts and explains the zigzag instability found by a numerical stability analysis in a companion paper (Otheguy, Chomaz & Billant, J. Fluid. Mech. vol. 553, 2006, p. 253). The zigzag instability results from the coupling between the bending perturbations of each vortex and the external strain that one vortex induces on the other S =G/2pb2, where G is the circulation of the vortices. The analysis predicts that the maximum growth rate of the instability is twice the strain S and that the most unstable vertical wavelength ? scales as the buoyancy length, defined by LB =G/paN, multiplied by the ratio b/a, i.e. ? ? Fhb, where Fh =G/pa2N is the horizontal Froude number. The asymptotic results are in very good agreement with the numerical results. © 2007 Cambridge University Press.

Domains: Fluid mechanics [physics.class-ph]; Fluids mechanics [physics.class-ph]

Pantxika Otheguy, Paul Billant, Jean-Marc Chomaz. Theoretical analysis of the zigzag instability of a vertical co-rotating vortex pair in a strongly stratified fluid. Journal of Fluid Mechanics, 2007, 584 (august), pp.103-123. ⟨10.1017/s0022112007006295⟩. ⟨hal-01023342⟩