Boundary surface dynamics: An algorithm for stratified geostrophic flows (Q1326689)

Assuming three-dimensional stratified geostrophic vortices of finite volume and potential vorticity of arbitrary vertical structure but piecewise-constant distribution in the horizontal direction, we derive equations for the velocity field in terms of surface integrals over the boundary of the vortex regions. Using conservation of quasi-geostrophic potential vorticity and the concepts of contour dynamics, the three- dimensional problem is reduced to the Lagrangian evolution of the boundary surface enclosing the vortex region, thus decreasing the number of dimensions by one. The equations are discretized in space and time giving a simple and robust algorithm for the evolution of the flow with specified initial conditions.