CONVECTIVE FLOW IN BAROCLINIC VORTICES

Convective flow in baroclinic vortices is studied analytically, taking viscosity nu and thermal diffusivity kappa into account. The meridion al circulation depends strongly on the Prandtl number Pr = nu/kappa. I f Pr > 1, there is upwelling in the interior of the vortex and the ver tical heat diffusion is therefore inhibited by advection. The radial f low is inward in most of the vortex, which is compensated by outward f low in a viscous boundary layer just below the surface. The authors fo cus on the strongly nonlinear regime, when the background stratificati on is much weaker than that of the vortex. It is found that the nonlin ear equation governing the flow in the limit Pr much greater than 1 ha s a class of exact time-dependent solutions. In this class the evoluti on of the vertical temperature profile is determined by Burger's equat ion, whereas the horizontal profile is determined by the Liouville equ ation. Both these equations can be solved analytically.