SOME EXACT-SOLUTIONS TO THE SEMI-GEOSTROPHIC EQUATIONS FOR UNIFORM POTENTIAL VORTICITY FLOWS

Some exact, nonlinear solutions to the unapproximated semi-geostrophic invertibility problem are noted for flows with uniform potential vorticity. One class of these solutions corresponds to an isolated homogeneous intrusion of fluid in a stratified background flow; the other represents a baroclinic point vortex analogous to the singular solution of the Laplacian which arises in the related quasigeostrophic problem. The isolated intrusion solution is the formal, axisymmetric extension of the twodimensional case given by Gill (1981). Using the conformal mapping method introduced by Gill, a twodimensional, barotropic solution to the semi-geostrophic equations is obtained. This can be interpreted as an exact solution corresponding to uniform barotropic flow around an obstacle. © 1991, Taylor & Francis Group, LLC. All rights reserved.