## Abstract

The three-dimensional nature of breaking Rossby waves in the polar wintertime stratosphere is studied using an idealized global primitive equation model. The model is initialized with a well-formed polar vortex, characterized by a latitudinal band of steep potential vorticity (PV) gradients. Planetary-scale Rossby waves are generated by varying the topography of the bottom boundary, corresponding to undulations of the tropopause. Such topographically forced Rossby waves then propagate up the edge of the vortex, and their amplification with height leads to irreversible wave breaking.

These numerical experiments highlight several nonlinear aspects of stratospheric dynamics that are beyond the reach of both isentropic two-dimensional models and fully realistic GCM simulations. They also show that the polar vortex is contorted by the breaking Rossby waves in a surprisingly wide range of shapes.

With zonal wavenumber-1 forcing, wave breaking usually initiates as a deep helical tongue of PV that is extruded from the polar vortex. This tongue is often observed to roll up into deep isolated columns, which, in turn, may be stretched and tilted by horizontal and vertical shears. The wave amplitude directly controls the depth of the wave breaking region and the amount of vortex erosion. At large forcing amplitudes, the wave breaking in the middle/lower portions of the vortex destroys the PV gradients essential for vertical propagation, thus shielding the top of the vortex from further wave breaking.

The initial vertical structure of the polar vortex is shown to play an important role in determining the characteristics of the wave breaking. Perhaps surprisingly, initially steeper PV gradients allow for stronger vertical wave propagation and thus lead to stronger erosion. Vertical wind shear has the notable effect of tilting and stretching PV structures, and thus dramatically accelerating the downscale stirring. An initial decrease in vortex area with increasing height (i.e., a conical shape) leads to focusing of wave activity, which amplifies the wave breaking. This effect provides a geometric interpretation of the “preconditioning” that often precedes a stratospheric sudden warming event. The implications for stratospheric dynamics of these and other three-dimensional vortex properties are discussed.

*Corresponding author address:* Dr. Lorenzo Polvani, Dept. of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027.

Email: polvani@columbia.edu