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Chaotic mixing in dynamically consistent flows obtained as numerical solutions of the barotropic vorticity equation was investigated. The barotropic model is a forced-dissipative system which simulates an idealized polar vortex, especially in the wintertime upper stratosphere. A typical example of chaotic mixing is obtained for the quasi-periodic flow. Effective, irreversible mixing occurs through stretching and folding process outside of the polar vortex, and inside as well. The transport barriers are identified precisely as invariant tori in the Poincare sections. In addition to the barrier associated with steep potential vorticity gradients on the edge of the polar vortex, transport barriers which is not related to the potential vorticity gradient is found inside the polar vortex. Furthermore, it is revealed that the structure obtained in the quasi-periodic flow is relevant to flows that are weakly aperiodic.
Relevance of the transport barrier found in the model experiment to the real atmosphere was investigated using horizontal wind data on isentropic surfaces. We examined in the wintertime upper stratosphere in the southern hemisphere, where irregularity of the flow is considerably weak. When the 4-day wave has a large amplitude, distributions of finite-time Lyapunov exponents show a large inhomogeneity inside the polar vortex. Effective mixing through stretching and folding process is seen on about 60-70°, where the Lyapunov exponent is high. But particles are not mixed in the other region. When the wave is not seen, on the other hand, Calculation of finite-time Lyapunov exponents and particle advections inside the vortex suggest that mixing does not occur.