Application to the Polar Vortex

Relative dispersion is calculated for the polar vortex flow by initializing a regularly spaced latitude-longitude grid and advecting the grid nodes using the UKMO winds.  The resulting scalar fields are plotted against initial conditions to reveal the geometry of the flow at the time of the grid initialization.  In the following two plots, a logarithmic scaling is used due to the exponential separation of nearby trajectories in the flow.
forward time relative dispersion, 11 October 
backward time relative dispersion, 11 October

Note the local minima (blue) of relative dispersion at the core of the jet and in the vortex core (the bottom edge of the images).  The filaments of local maxima (red) are highly suggestive of the chaotic advection mechanism.  This can be appreciated more by plotting the two calculations together:
(click on this frame and hit the reload button to re-animate)

Forward time maxima are color-coded blue and backward time maxima are magenta.

Relative dispersion identifies material curves to reveal a geometry that agrees well with the chaotic advection paradigm.  The intersections of these curves near the crests in the jet meanders correspond to the hyperbolic fixed points generating the manifolds in the standard theory, whereas other intersections define lobes.  The evolution of the lobes in time may be tracked to study the nature of transport in the surf zone.  The lack of a curve of local maxima that crosses the jet suggests that little transport occurs across the jet via the chaotic advection mechanism.