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Dynamical processes of transport and mixing around the wintertime stratospheric polar vortex have been examined in connection with the Antarctic ozone hole A transport barrier exists at the edge of the polar vortex and air within the vortex is isolated from outside. Studies on isentropic trajectories by using analyzed winds (Bowman 1993) and three dimensional models (Pierce and Fairlie 1993) showed that chaotic mixing occurs inside and outside of the vortex, respectively, based on the exponential growth of material contours and the patterns of stretching and folding.
Pierrehumbert (1991) applied the concept of chaotic mixing to geophysical flows; he investigated a planetary wave motion with a small periodic perturbation in a two-dimensional channel domain and showed the evidence of chaotic mixing in the flow. Mixing in two-dimensional nondivergent flows has been studied in relation with Hamiltonian dynamics for fluid particles.
In this study, the stratospheric polar vortex is idealized as a solution with quasi-periodic time dependence of a nondivergent barotropic model, and horizontal mixing around the vortex is investigated. The time periodicity enables us to use the same kind of analysis methods as in the kinematical studies of Hamiltonian dynamics. The flow field in our model has dynamical consistency because it is obtained in a direct numerical simulation of a full dynamical equation more akin to the atmosphere than previous kinematical models. In addition, the mixing process in the quasi-periodic flow is compared with that in a more realistic aperiodic flow of similar pattern which is obtained in the same model.
In the flows of our model, eastward propagating planetary waves generated through barotropic instability are dominant. The situation is close to that in the upper stratosphere of the southern hemisphere where the 4-day wave is often observed. The 4-day wave appears in the upper stratosphere in winter (Venne and Stanford 1979), more evidently in the southern hemisphere than in the northern hemisphere. It is dominated by zonal wavenumbers from 1 to 4, traveling eastward with the same phase speed. Observational and theoretical studies are summarized in Allen et al. (1997), and Manney et al. (1998). Relevance of the results in the model experiment to the real atmosphere is investigated using the same methods on isentropic surfaces.