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Transport and separatrices in time-dependent flows

Citation

Du Toit, Philip C. (2010) Transport and separatrices in time-dependent flows. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:10072009-165901284

Abstract

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, and flows in the phase space of second order dynamical systems. 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 FTLE-LCS, 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. Beyond geophysical flows, we also study transport in the phase space of a coupled oscillator model for biomolecules. Before we can analyze transport in this model, we first introduce an appropriate model reduction that captures the relevant statistics of the full system. In the reduced model, we see that transport is again mediated by the process of horseshoe dynamics in a perturbed homoclinic tangle. We also consider some theoretical aspects of FTLE-LCS, including the relationship between LCS and stable/unstable manifolds, the invariance of LCS, and the possibility of an evolution equation describing the motion of the LCS. A parallelized software for computing FTLE is also introduced.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Lagrangian coherent structures, finite time Lyapunov exponents, homoclinic tangle, hurricanes, ocean dynamics, mesoscale eddies, nonlinear oscillators
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Control and Dynamical Systems
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Marsden, Jerrold E.
Thesis Committee:
  • Marsden, Jerrold E. (chair)
  • Doyle, John Comstock
  • Murray, Richard M.
  • Dabiri, John O.
Defense Date:9 July 2009
Author Email:dutoit (AT) caltech.edu
Funders:
Funding AgencyGrant Number
AFOSRFA9550-07-C-0024
ONRN00014-04-1-0534
Record Number:CaltechTHESIS:10072009-165901284
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:10072009-165901284
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5293
Collection:CaltechTHESIS
Deposited By: Philip Du Toit
Deposited On:26 May 2010 21:56
Last Modified:26 Dec 2012 03:18

Thesis Files

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PDF (Abstract and Contents) - Final Version
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PDF (Chapter 1: Introduction) - Final Version
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PDF (Chapter 2: Homoclinic points and the horshoe map - a reprise) - Final Version
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PDF (Chapter 3: FTLE, LCS, and five examples) - Final Version
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PDF (Chapter 4: LCS and the perturbed pendulum) - Final Version
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PDF (Chapter 5: LCS in a model for Mediterranean eddies) - Final Version
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PDF (Chapter 6: LCS and hurricanes) - Final Version
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PDF (Chapter 7: LCS and the global ocean) - Final Version
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PDF (Chapter 8: Flow of a biomolecule) - Final Version
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PDF (Chapter 9: Properties of the LCS) - Final Version
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PDF (Chapter 10: Numerical considerations) - Final Version
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PDF (Chapter 11: Conclusion) - Final Version
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PDF (Appendix A: Newman - Software for computing FTLE in geophysical applications) - Final Version
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PDF (Bibliography) - Final Version
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PDF (Title page and acknowledgements) - Final Version
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PDF (Complete thesis in a single PDF file) - Final Version
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