Time-dependent dynamical systems and geophysical flows

• Main Author: Lekien, Francois Paul
• Format: Thesis
• Language: English
• Published: California Institute of Technology 2003
• Subjects: open-boundary modal analysis; hyperbolic; manifold deformation framework; pollution control; release time; high-frequency radar; time-dependent; Control and Dynamical Systems; Lyapunov exponent; OMA; hyperbolicity; dynamical systems; North Atlantic
• Online Access: https://dx.doi.org/10.7907/a83e-vz73; https://resolver.caltech.edu/CaltechETD:etd-04082003-180353

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.