N-Vortex Problems

University Of Southern California, Los Angeles CA

Investigators

Abstract

Discrete models of the Euler equations governing fluid mechanics will be analyzed with the goal of understanding high Reynolds number turbulent flows. The comprehensive approach will involve a combination of mathematical analysis of Hamiltonian dynamical systems, physical modeling based on discrete particle representations of the Euler equations, and high performance computing. The mathematical problem is of N-body type, thus numerical algorithm development for these systems and dynamical systems visualization techniques will be an essential component of the work carried out under this award. The four main projects described in the proposal are each designed to develop new analytical techniques in dynamical systems theory, test current techniques on models that are physically well grounded, develop new numerical algorithms and visualization methods for particle interaction problems, and push the models closer towards applications. This project involves the development of discrete models for fluid flow, using a combination of mathematical tools and high performance computing. One major emphasis will be on studying these models on the surface of a sphere, both rotating and non-rotating, a problem which has direct applications to the flow in a planetary atmosphere on such large scales that the curvature of the planet plays a role in the dynamics. This problem is potentially of great importance to the understanding of environmental processes in the atmospheres and oceans of Earth and to the large vortices, including the Red Spot, observed in the atmosphere of Jupiter.