BAROCLINIC INSTABILITY OF KIRCHHOFF ELLIPTIC VORTEX

The linear instability of Kirchhoff's elliptic vortex in a vertically stratified rotating fluid is investigated using the quasi-geostrophic, f-plane approximation. Any elliptic vortex is shown to be unstable to baroclinic disturbances of azimuthal wavenumber m = 1 (bending mode) and m = 2 (elliptical deformation). The axial wavenumber of the unstab le bending mode approaches lambda(c) = 1.7046 in the limit of small el lipticity, indicating that it is a short-wave baroclinic instability. The instability occurs when the bending wave rotates around the vortex axis with angular velocity identical to the rotation rate of the undi sturbed elliptic vortex. On the other hand, the wavenumber of the elli ptical deformation mode approaches zero in the same limit, showing tha t it is a long-wave sideband instability.