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

A new, versatile, and efficient numerical algorithm for three-dimensio nal quasi-geostrophic calculations using contour dynamics/surgery is d escribed 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 repr esentation in fluid dynamics, allowing one to focus resolution on the most dynamically active parts of the flow, i.e. regions of high potent ial-vorticity gradients. The algorithm is generally applicable to a wi de range of idealized atmospheric and oceanic flows. Important effects of compressibility, variable stratification, surface temperature grad ients and topography are included. It is applied in this paper to stud y how a three-dimensional barotropic vortex responds to topographic fo rcing at the bottom boundary or tropopause. Two regimes of wave breaki ng are found: the first is local wave breaking, which occurs near the lower boundary for strong topographic forcing; the second is remote wa ve breaking, which occurs at the upper levels for weak topographic for cing. 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 t o Prandtl's ratio (as one might expect from geostrophic turbulence), f eatures resulting from wave breaking in a compressible atmosphere with weak vertical shear tend to have a nearly barotropic structure.