Journal of Fixed Point Theory and Applications

, Volume 7, Issue 2, pp 351-384

First online:

Horseshoes in hurricanes

  • Philip C. du ToitAffiliated withNumerica Corporation Email author 
  • , Jerrold E. MarsdenAffiliated withCalifornia Institute of Technology, Control and Dynamical Systems

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The method of using Finite Time Liapunov Exponents (FTLE) to extract Lagrangian Coherent Structures (LCS) in aperiodic flows, as originally developed by Haller, is applied to geophysical flows. In this approach, the LCS are identified as surfaces of greatest separation that parse the flow into regions with different dynamical behavior. In this way, the LCS reveal the underlying skeleton of turbulence. The time-dependence of the LCS provides insight into the mechanisms by which fluid is transported from one region to another. Of especial interest in this study is the utility with which the FTLE-LCS method can be used to reveal homoclinic and horseshoe dynamics in aperiodic flows.

The FTLE-LCS method is applied to turbulent flow in hurricanes and reveals LCS that delineate sharp boundaries to a storm. Moreover, intersections of the LCS define lobes that mediate transport into and out of a storm through the action of homoclinic lobe dynamics. Using the FTLE-LCS method, the same homoclinic structures are seen to be a dominant transport mechanism in the Global Ocean, and provide insights into the role of mesoscale eddies in enhancing lateral mixing.

Mathematics Subject Classification (2010)

37C10 86-08 76-04


Finite time Lyapunov exponents Lagrangian coherent structures homoclinic tangles hurricanes mesoscale ocean eddies transport mixing