Nonlinear Processes in Oceanic and Atmospheric Flows

Presentation

Hurricanes, Homoclinic Tangles, and Horseshoes.

Author: Philip Du Toit, California Institute of Technology.

Names and affiliation of other authors:
Jerrold Marsden
California Institute of Technology

Oral or poster: Poster

Downloadable poster file:

Hurricanes, Homoclinic Tangles, and Horseshoes.

(pdutoit_poster.pdf, 6768059 bytes)

Abstract:
Recently, Lagrangian methods using Finite Time Liapunov Exponents (FTLE) have been developed to uncover the underlying skeletal structure that dictates how transport occurs in aperiodic flows. Interestingly, these Lagrangian methods reveal well-defined surfaces in the flow that act as barriers to transport and separate regions of different dynamical behavior.
In this study, we apply this method of using FTLE to extract Lagrangian Coherent Structures (LCS) to both ocean flows and the manifestly turbulent wind field data for hurricanes. A main result is the discovery of sharply defined surfaces in the flow surrounding the hurricane that govern transport both into and out of the storm. Furthermore, the evolution of these surfaces indicate very plainly that transport in the large-scale flow occurs via the mechanism of lobe dynamics associated with a homoclinic tangle, a process well-understood in classical geometric dynamics. The LCS method reveals that transport in hurricanes is a low-dimensional process whose salient features are adequately described by a very simple two-dimensional dynamical system that exhibits a chaotic tangle concomitant with a perturbed homoclinic connection. Results for the simple model not only provide an insightful comparison with the LCS results for the full hurricane data set, but also illustrate the utility of the LCS method for identifying homoclinic tangles in aperiodic flows.

*Satellite images from NASA and ESA

Nonlinear Processes in Oceanic and Atmospheric Flows. July 2-4, 2008. Castro Urdiales, Cantabria, Spain.