We consider the three-dimensional dynamics of a breaking Rossby wave on the edge of a cylindrical, axisymmetric vortex, as a representation of breaking planetary waves on the winter stratospheric polar vortex. A complete understanding of the mechanisms involved is not only important for, e.g., applications to the confinement of chemical species within the stratospheric vortex, but also provides insight into possible ways in which the dynamics of the perturbed vortex may influence the troposphere below.

Here, we extend the work of Dritschel and Saravanan (1994) and Polvani and Saravanan (2000) and examine in detail the role of the vortex edge width on Rossby wave propagation and breaking. We examine wave breaking both in an idealized contour dynamics model, as well as in a full primitive equation model in spherical geometry. The edge width, as well as the lower boundary wave forcing amplitude, is varied as an external parameter.

The results show that, in both the weakly forced quasi-linear regime and in the strongly forced nonlinear regime, wave propagation and the deceleration of the vortex is reduced as the edge width is increased. This effect is shown most clearly by the contour dynamics model, where the efficiency of the method allows a full exploration of the parameter space of forcing amplitude and edge width.

The primitive equation model confirms the contour dynamics results, and highlights direct implications for stratospheric modeling in more comprehensive models. At a fixed high resolution (e.g. T170), there is again weaker vortex deceleration with a broader edge width. On the other hand, when an initial state is specified to represent the steep vortex edge seen in observations, the use of low resolution (e.g. T42) causes a diffusion, or broadening, of the edge, with a consequent reduction of wave propagation. The implication is that low resolution climate models, by underresolving the polar vortex edge width, may seriously underestimate wave propagation in the stratosphere.