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Time-Dependent Dynamical Systems and Geophysical Flows


Lekien, Francois Paul (2003) Time-Dependent Dynamical Systems and Geophysical Flows. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/A83E-VZ73.


This thesis presents a dynamical systems approach to transport and mixing in geophysical flows. First, new algorithms are developed that allow one to study a dynamical system that is described in a variety of ways such as by means of observational data or numerical simulations of differential equations.

Next, methods available to study non-autonomous systems, such as hyperbolic trajectories and Lagrangian coherent structures, are developed. These concepts are applied to examples of interests: Monterey Bay, the coast of Florida and the circulation in the North Atlantic. Combining accurate current measurements and recent developments in dynamical systems theory provides new and original answers to many problems, such as the minimization of the impact of released contaminants in a coastal area or the optimization of the coverage by a group of drifters.

The appendices give details about MANGEN, a software package developed to produce the numerical results of this thesis. Some projects that make use of its algorithms, such as the dissociation rate of a molecule and efficient space mission design, are also described.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:dynamical systems; high-frequency radar; hyperbolic; hyperbolicity; Lyapunov exponent; manifold deformation framework; OMA; open-boundary modal analysis; pollution control; release time; time-dependent
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. (advisor)
  • Murray, Richard M. (advisor)
Thesis Committee:
  • Marsden, Jerrold E. (chair)
  • Leonard, Anthony
  • Haller, George
  • Mezic, Igor
  • Murray, Richard M.
Defense Date:12 March 2003
Record Number:CaltechETD:etd-04082003-180353
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1304
Deposited By: Imported from ETD-db
Deposited On:10 Apr 2003
Last Modified:05 May 2021 23:52

Thesis Files

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