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- Title
Theoretical analysis of the zigzag instability of a vertical co-rotating vortex pair in a strongly stratified fluid.
- Authors
PANTXIKA OTHEGUY; PAUL BILLANT; JEAN-MARC CHOMAZ
- Abstract
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 bcompared to their radius a(ba). 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= ?/2 ? b2, where ? is the circulation of the vortices. The analysis predicts that the maximum growth rate of the instability is twice the strain Sand that the most unstable vertical wavelength ? scales as the buoyancy length, defined by LB= ?/?aN, multiplied by the ratio b/a, i.e. ? Fhb, where Fh= ?/?a2Nis the horizontal Froude number. The asymptotic results are in very good agreement with the numerical results.
- Subjects
VORTEX motion; FLUID dynamics; PERTURBATION theory; FLUID mechanics; AERODYNAMICS; EDDIES
- Publication
Journal of Fluid Mechanics, 2007, Vol 584, Issue 1, p103
- ISSN
0022-1120
- Publication type
Article
- DOI
10.1017/S0022112007006295