Stochastic Analysis of Vortex Filaments

点击翻译按钮获取中文摘要

BessaihDMS-0608494 The investigator studies random vortex filaments and theirrelationship to turbulent flows. She develops a rigorousstochastic description of filament structures, studies filamentdynamics, and examines mean field limits for interacting vortexfilaments and their relation to the Euler equations. WhileBrownian semimartingales are the stochastic processes that havereceived more attention in other studies of random vortexfilaments, here extension to stochastic processes withmultifractal structure or intermittency features is considered. The underlying problem of turbulence is fundamental. Studentsare involved in the project. Random vortex filaments -- roughly speaking, vortical tubesof fluid moving under the influence of a random process -- are amodel for the motion of fluids that could shed some light on thedevelopment and evolution of turbulence in fluid flows. Theinvestigator studies random vortex filaments, considering theirstructure, their dynamics, the behavior of large collections ofvortex filaments, and their relationship to the Euler equations,a well-known model of fluid flows. Students are involved in theproject. Better mathematical models of turbulence in fluid flowscould lead to a better understanding of the mechanisms ofturbulence. This in turn would improve our understanding ofatmosphere and ocean circulation, with possible consequences forweather prediction, and of fluid flows in engineeringapplications, such as the design of faster and more economicallyoperated ships, planes, and vehicles.