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Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex

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Figure 1b shows that the Mtion is related to fluid regions trapping fluid parcels in theirinterior and isolating them from the surrounding fluid, as forinstance is the case for the circulating strong jet forming thebility of revealing vortices present in the
Figure 1. (a) Stable (blue) and unstable (red) manifolds of the nor-mally hyperbolic invariant curve in Eq
Figure 2. M calculated on 15 August 1979 at 00:00:00 UTC: (a) using a 2-D approach where particle trajectories are constrained to the850 K potential temperature level and τ = 5 days; (b) M computation for τ = 5 days using a full 3-D computation of trajectories, and it isrepresented at a constant height level of h = 31.3 km (which corresponds approximately to the 850 K isentropic surface); (c) the same aspanel (a) with τ = 10 days; (d) the same as panel (b) with τ = 10 days; (e) the same as panel (a) with τ = 20 days; (f) the same as panel (b)with τ = 20 days.
Figure 3. M(d) calculated on 15 August 1979 at 00:00:00 UTC: (a) using a 2-D approach where particle trajectories are constrained to the330 K potential temperature level and τ = 5 days; (b) the same with τ = 10 days; (c) M calculated for τ = 5 days using a 3-D computationof trajectories and represented at a constant height level of h = 10 km (which corresponds approximately to the 330K isentropic surface); the same with τ = 10 days.
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