Instabilities of baroclinic vortices in stratified-rotating fluids

Abstract eng:
We investigate the stability of an axisymmetric pancake vortex in a continuously stratified and rotating fluid. The characteristics and domains of existence of the different instabilities are determined as a function of the Froude number Fh , Rossby number Ro, aspect ratio α and Reynolds number Re. The centrifugal instability is almost independent of the aspect ratio of the vortex due to its short-wavelength nature and depends mostly on the Rossby number Ro and the buoyancy Reynolds number R = ReFh2 . The shear instability exists for the azimuthal wavenumber m = 2 only when Fh /α is below a threshold depending on Ro. This condition comes from confinement effects along the vertical. The shear instability transforms into a mixed baroclinic-shear instability when the Burger number Bu = α2 Ro2 /(4Fh2 ) is smaller than unity. The baroclinic instability develops when Fh /α|1 + 1/Ro| > 1.46 in qualitative agreement with an analytical model.

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