Quasigeostrophic, tilted spheroidal vortices

Vortex motions in a stably stratified rotating fluid are considered theoretically, based on the quasigeostrophic approximation. A class of exact solution is obtained, which represents a tilted spheroidal volume with uniform potential vorticity embedded in an otherwise quiescent fluid of infinite extent. The spheroid rotates steadily about the vertical axis, where the angular velocity is independent of the inclination angle of the axis of symmetry from the vertical axis, We study. the stability of these solutions against infinitesimal disturbances. Highly elongated prolate spheroids ale shown to he unstable if the inclination angle is large. In contrast, oblate spheroids of certain aspect ratio are unstable ei en if the inclination angle is very small. This instability is caused Ly resonance between the tilted rotation and other disturbance modes.