Chaotic Mixing and Transport Barriers in an Idealized Stratospheric Polar Vortex

Ryo Mizuta Department of Geophysics, Kyoto University, Kyoto, Japan

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Shigeo Yoden Department of Geophysics, Kyoto University, Kyoto, Japan

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Abstract

Chaotic mixing processes and transport barriers around the wintertime stratospheric polar vortex are investigated with an idealized barotropic model, previously used by Ishioka and Yoden. A barotropically unstable jet is forced in order to obtain a fluctuating polar vortex. A flow with quasiperiodic time dependence and an aperiodic flow with similar behavior are investigated using several Lagrangian methods.

A typical chaotic mixing process is observed in the quasiperiodic flow, resulting in effective mixing inside and outside of the polar vortex. The mixing regions are on the critical latitudes of several planetary waves that grow through barotropic instability. Poincaré sections give accurate locations of chaotic mixing regions, and transport barriers are identified as the edges of invariant torus regimes. In addition to the transport barriers associated with strong potential vorticity gradients, another type of transport barrier exists, which is not related to the steep potential vorticity gradient.

Chaotic mixing is dominant also in the aperiodic flow. Comparing with the quasiperiodic flow, an aperiodic flow with the same wave energy has a higher average Lyapunov exponent. This arises because the area involved in chaotic zones increases. The evolution of the correlation function is also more typical of a chaotic zone. Isolated regions are found near the center of the polar vortex, which can be explained by the invariant tori in the Poincaré sections of the quasiperiodic flow. Implications of the results for the observed “4-day wave” in the upper stratosphere are discussed.

Corresponding author address: Shigeo Yoden, Department of Geophysics, Kyoto University, Kyoto 606-8502, Japan. Email: yoden@kugi.kyoto-u.ac.jp

Abstract

Chaotic mixing processes and transport barriers around the wintertime stratospheric polar vortex are investigated with an idealized barotropic model, previously used by Ishioka and Yoden. A barotropically unstable jet is forced in order to obtain a fluctuating polar vortex. A flow with quasiperiodic time dependence and an aperiodic flow with similar behavior are investigated using several Lagrangian methods.

A typical chaotic mixing process is observed in the quasiperiodic flow, resulting in effective mixing inside and outside of the polar vortex. The mixing regions are on the critical latitudes of several planetary waves that grow through barotropic instability. Poincaré sections give accurate locations of chaotic mixing regions, and transport barriers are identified as the edges of invariant torus regimes. In addition to the transport barriers associated with strong potential vorticity gradients, another type of transport barrier exists, which is not related to the steep potential vorticity gradient.

Chaotic mixing is dominant also in the aperiodic flow. Comparing with the quasiperiodic flow, an aperiodic flow with the same wave energy has a higher average Lyapunov exponent. This arises because the area involved in chaotic zones increases. The evolution of the correlation function is also more typical of a chaotic zone. Isolated regions are found near the center of the polar vortex, which can be explained by the invariant tori in the Poincaré sections of the quasiperiodic flow. Implications of the results for the observed “4-day wave” in the upper stratosphere are discussed.

Corresponding author address: Shigeo Yoden, Department of Geophysics, Kyoto University, Kyoto 606-8502, Japan. Email: yoden@kugi.kyoto-u.ac.jp

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