Boundary Surface Dynamics: An Algorithm for Stratified Geostrophic Flows

Abstract

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 quasigeostrophic 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. The model is used to study the interaction of two identical cylindrical vortices of finite height in a spatially unbounded fluid. For vortices at the same level the simulations show that if the horizontal scale is larger than the internal radius of deformation, filamentation is virtually suppressed and the resulting structure is a compact cylindrical vortex of ellipse-like cross section. For vortices at different levels the interaction results in a structure of considerable horizontal and vertical complexity due to the combined effects of merger and alignment processes acting together.