Quasigeostrophic ellipsoidal vortices in a two-dimensional strain field

Vortex motions in a stably stratified rotating fluid are considered theoretically, based on the quasigeostrophic approximation. A class of exact stationary solution is obtained, which represents an ellipsoidal volume with uniform potential vorticity Qa embedded in a two-dimensional uniform strain field (e) over cap with uniform background vorticity 2<(gamma)over cap>. In a pure strain held (<(gamma)over cap> = 0), stationary solutions are allowed for \(e) over cap/Q(0)\ < about 0.15. Similarly, stationary solutions are allowed for (e) over cap/Q(0) > shout -0.1 in a simple shear flow (<(gamma)over cap> = (e) over cap). We study the stability of these exact solutions against infinitesimal disturbances. In a pure strain field: highly elongated ellipsoids are shown to be unstable to Lame-modes whose order m is higher than 2. In a simple shear now, a highly elongated ellipsoid whose major asis is perpendicular to the Aom direction, is unstable, whereas any ellipsoidal vortex seems to be stable, if the major axis is parallel to the now direction.