Tracer Advection

Tracer advection, polar stereographic projection
1 October - 11 October
Tracer advection, equidistant cylindrical projection
1 October - 11 October

Tracers are advected using the winds from the UKMO stratospheric analysis.  In the above figures, advected tracers are color coded according to their initial latitudes.  Filaments of fluid near the vortex edge are ejected (light blue), and some filaments of midlatitude air are drawn near the jet (yellow and orange).

Two cat's eye vortices associated with the dominant wavenumber 2 Rossby wave are evident.  A chaotic advection transport mechanism is suggested by the tracer fields.  The goal, then, is to locate the distinguished material curves that play the role of the invariant manifolds in this flow.  In traditional chaotic advection studies, infinite time formulation of the problem and the presence of a hyperbolic Lagrangian trajectory allow for the identification of associated invariant manifolds as the relevant distinguished material curves.  We must apply a finite-time formulation of these ideas.

The main difficulty in this problem is that fixed time slices of the Eulerian velocity field do not yield hyperbolic stagnation points, as any such region of hyperbolicity is advected eastward with the jet.  No dominant phase speed exists that would allow us to shift to a moving reference frame in which the stagnation points will appear.  We must therefore attempt to locate regions of strong hyperbolicity by another means.