N-Vortex Problems: Analysis, Computation, and Data Acquisition

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The project focuses on a wide range of N-vortex problems from dynamical systems theory, based on discrete vortex representations of the Euler equations of incompressible fluid mechanics. Emphasis will be placed on three topics: (1) The N-vortex problem on a rotating sphere with applications to atmospheric flows; (2) Analysis and data acquisition of global weather patterns; (3) N-body numerical algorithm development. Each is designed to develop new analytical and computational techniques in dynamical systems theory, test current techniques on models that are physically well grounded, develop new numerical algorithms that conserve quantities we know should be conserved, and push the models closer towards applications mostly in oceanographic and atmospheric sciences, but also in molecular modeling where some of the same underlying issues pertain (albeit with Hamiltonians of a different form). In many cases, techniques that have been developed for N-body problems in the celestial mechanics context will be exploited and adapted for use on this class of discrete vortex problems. Tools developed fall under the general category of high-performance computing in the context of Hamiltonian and Lagrangian mechanical systems and the topics will be relevant in the development and formulation of global circulation models for the atmosphere and oceans. The data acquisition portion of the project focuses on the understanding of global weather patterns and the connection between these patterns and the transport and mixing of passive and active scalars such as environmental pollutants, oceanographic biota, and atmospheric ozone.