This paper presents results from a single-layer, shallow-water, 100-day model integration that reproduces many features of the wintertime stratosphere, particularly in the tropics, more realistically than earlier single-layer integrations. The advective transport of passive tracers by breaking Rossby waves is examined using a new polar-vortex-following coordinate system and a technique for advecting material contours, in which they are followed very accurately using the contour-dynamics algorithm of Dritschel. Unlike any Eulerian tracer advection scheme, the technique for advecting material contours has no numerical diffusion and can handle the ultrafinescale, exponentially shrinking tracer features characteristic of chaotic advective transport or “stirring,” which is conspicuous here in the stratospheric “surfzone.” The technique may become important as a benchmark for quantitative comparison with Eulerian tracer advection schemes, such as those used in general circulation models.
Averages with respect to the vortex-following coordinate system give a clearer picture of the gross features of the tracer transport than conventional Eulerian zonal averages, because the reversible displacements associated with undulating Rossby waves are largely eliminated. Results indicate that the edge of the polar vortex acts as a flexible, “Rossby elastic” barrier to eddy transport of air from the surf zone into the vortex, with air well inside the vortex completely isolated for the entire 100 days. This last point is precisely demonstrated by results from the technique for advecting material contours. Erosion of material from the vortex during days 30 to 100 of the model integration was not more than about 16% of the area of the model's surf zone, counted as the area between 30°N and 60°N. The model integration also shows, more realistically than earlier single-layer integrations, a partial barrier to exchange of air between the tropics and middle latitudes.
Results using the technique for advecting material contours also show that material contours in the surf zone lengthen exponentially rapidly with an e-folding time of about 4 days during the first 30 days. Material contours in the tropics lengthen only slowly, the contour farthest within the tropics lengthening by a factor of only 2 during the first 30 days. Material contours embedded in the vortex edge behave in an almost purely undular manner and hardly lengthen at all, except near the end of 100 days of integration when the vortex is violently disturbed and relatively strongly eroded albeit still showing a perfectly isolated core. The minimum distance between contours is also examined and shows exponentially shrinking behavior in the surf zone with a fastest e-folding time of about 1 day, dominated by what happens in the regions of strongest stirring. The relevance to real stratospheric ozone depletion and the “flowing processor hypothesis” is discussed.