Visualizing and Quantifying Transport in Hurricanes.

Flows surrounding hurricane storms are manifestly complex. The chaotic nature of individual particle trajectories forestalls attempts to understand material transport by appealing to the Eulerian velocity field or particle trajectories alone. However, even in these complex flows, we demonstrate the existence of time-dependent coherent structures that govern the pathways for transport. These structures, called Lagrangian Coherent Structures (LCS), are moving barriers to transport in the flow and define the boundaries of almost invariant regions. They also act as separatrices in that they separate flow regions with different dynamical behavior. Given the velocity field, we extract the LCS numerically through computation of the finite time Lyapunov exponent which is a measure of local stretching in the flow. Once computed, the LCS allow us to visualize and understand the essential mechanisms underlying transport in the flow. We illustrate these results through several examples in both atmospheric and oceanic flows with special emphasis on the insights gained from transport structures in hurricane flows. In particular, we see that transport in the flow surrounding hurricanes and tropical storms occurs via the mechanism of lobe dynamics, a result that is not immediately obvious from inspection of the flow field.