Diagnosing hurricane mixing properties by Lagrangian techniques

Mixing processes in hurricanes can be described by the existence of persistent Lagrangian coherent structures (LCS), where particle movement across the LCS boundary is small. Time dependent scalar fields are calculated based on the separation of trajectories. Maximal values of the scalar fields show regions of maximal particle separation. Ridges of the scalar fields can be shown to be hyperbolic material lines for the time that they persist.

We look at the scalar fields created by finite time Lyapunov exponents (FTLEs), finite size Lyapunov exponents (FSLEs), and Elliptic-Parabolic-Hyperbolic partition (EPH), which are all measures of hyperbolicity. Distributions of the FTLEs can give a prediction of a mixing rate, which can be compared to an observed mixing rate that is estimated from the evolution of a passive scalar. The ridges of the FTLE field cannot be determined exactly, but an estimation of the ridges can give a representation of LCSs.

These methods are applied to an axisymmetric hurricane model. A combination of methods are used to analyze the mixing processes. In particular, we search for structures that are important for eyewall mixing processes. The structures are found as ridges of scalar fields, and flux across the structures is estimated. The length of time that the structure exists is also measured. Moreover, we study different atmospheric physical properties that are given in different regions that are separated by the LCS.

Several numerical difficulties arise in the calculations of the the LCS, and their existence or nonexistence is very sensitive to the resolution at which the scalar fields are calculated. Some structures appear only when the scalar field resolution is increased. We carefully examine the LCSs for increasing levels of resolution in both the original hurricane model as well as in the scalar fields derived from the model.