THE INSTABILITY AND BREAKDOWN OF TALL COLUMNAR VORTICES IN A QUASI-GEOSTROPHIC FLUID

We examine the linear stability of elliptical columns of uniform poten tial vorticity subject to two-dimensional (horizontal) straining withi n a rapidly rotating, stratified (quasi-geostrophic) fluid. We find th at horizontal straining can promote the exponential growth of three-di mensional disturbances when the vortex height-to-width aspect ratio ex ceeds, qualitatively, three times the ratio of the Coriolis parameter to the buoyancy frequency. This instability is not related to the usua l baroclinic instability which operates on shallow vortex columns whos e potential vorticity changes sign with height. The nonlinear developm ent of these instabilities is investigated numerically using a high-re solution contour surgery algorithm. Simulations are conducted for both a Boussinesq (ocean-like) fluid and a compressible (atmospheric-like) fluid having exponentially decreasing density with height. The simula tions reveal a generic nonlinear development that results in a semi-el lipsoidal baroclinic vortex dome at the lower surface and, in the case of a Boussinesq fluid, another such dome at the upper surface. The re lated problem of two interacting vortex columns is also examined. A ge neric three-dimensional instability and nonlinear development occurs n o matter how great the distance between the vortex columns, provided t hat they are sufficiently tall. Our results may bear upon the observed structure of many atmospheric and oceanic vortices, whose height-to-w idth aspect ratios are consistent with our findings. Remarkably, even strongly ageostrophic vortices, such as tropical cyclones, fit the pat tern. Our results furthermore re-open questions about the long-time na ture of freely decaying quasi-geostrophic turbulence, for which recent simulations indicate a progressive two-dimensionalization by vortex a lignment, while earlier simulations have indicated long-lived baroclin ic vortices, not unlike what we find here.