3-DIMENSIONAL QUASI-GEOSTROPHIC CONTOUR DYNAMICS, WITH AN APPLICATION TO STRATOSPHERIC VORTEX DYNAMICS

A new, versatile, and efficient numerical algorithm for three-dimensional quasi-geostrophic calculations using contour dynamics/surgery is described and illustrated. The numerical algorithm models the fluid as dissipationless (in contrast with conventional numerical models having artificial subgrid diffusivities) and is based on the Lagrangian representation in fluid dynamics, allowing one to focus resolution on the most dynamically active parts of the flow, i.e. regions of high potential-vorticity gradients. The algorithm is generally applicable to a wide range of idealized atmospheric and oceanic flows. Important effects of compressibility, variable stratification, surface temperature gradients and topography are included. It is applied in this paper to study how a three-dimensional barotropic vortex responds to topographic forcing at the bottom boundary or tropopause. Two regimes of wave breaking are found: the first is local wave breaking, which occurs near the lower boundary for strong topographic forcing; the second is remote wave breaking, which occurs at the upper levels for weak topographic forcing. The local wave breaking corresponds closely to the wave breaking seen in single-layer calculations, if the layer depth is chosen equal to a density scale-height. Rather than having an aspect ratio equal to Prandtl's ratio (as one might expect from geostrophic turbulence), features resulting from wave breaking in a compressible atmosphere with weak vertical shear tend to have a nearly barotropic structure.