Elliptic and zigzag instabilities on co-rotating vertical vortices in a stratified fluid

Abstract : We present a three-dimensional linear stability analysis of a couple of co-rotating vertical vortices in a stratified fluid. When the fluid is non-stratified, the two vortices are unstable to the elliptic instability owing to the elliptic deformation of their core. These elliptic instability modes persist for weakly stratified flow: Fh > 10, where Fh is the horizontal Froude number (Fh = Gh/pab2 N where Gh is the circulation of the vortices, ab their core radius and N the Brunt-Väisälä frequency). For strong stratification (Fh < 2.85), a new zigzag instability is found that bends each vortex symmetrically with almost no internal deformation of the basic vortices. This instability may modify the vortex merging since at every half-wavelength along the vertical, the vortices are alternatively brought closer, accelerating the merging, and moved apart, delaying the merging. The most unstable vertical wavelength ?m of this new instability is shown to be proportional to Fhbb, where bb is the distance between the vortices, implying that ?m decreases with increasing stratification. The maximum growth rate, however, is independent of the stratification and proportional to the strain S = Gb/2pbb2. These scaling laws and the bending motion induced by this instability are similar to those of the zigzag instability of a counter-rotating vortex pair in a stratified fluid. © 2006 Cambridge University Press.
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Pantxika Otheguy, Jean-Marc Chomaz, Paul Billant. Elliptic and zigzag instabilities on co-rotating vertical vortices in a stratified fluid. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2006, 553 (april), pp.253-272. ⟨10.1017/s0022112006008901⟩. ⟨hal-01023354⟩

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