The investigator studies random vortex filaments and their relationship to turbulent flows. She develops a rigorous stochastic description of filament structures, studies filament dynamics, and examines mean field limits for interacting vortex filaments and their relation to the Euler equations. While Brownian semimartingales are the stochastic processes that have received more attention in other studies of random vortex filaments, here extension to stochastic processes with multifractal structure or intermittency features is considered. The underlying problem of turbulence is fundamental. Students are involved in the project.

Random vortex filaments -- roughly speaking, vortical tubes of fluid moving under the influence of a random process -- are a model for the motion of fluids that could shed some light on the development and evolution of turbulence in fluid flows. The investigator studies random vortex filaments, considering their structure, their dynamics, the behavior of large collections of vortex filaments, and their relationship to the Euler equations, a well-known model of fluid flows. Students are involved in the project. Better mathematical models of turbulence in fluid flows could lead to a better understanding of the mechanisms of turbulence. This in turn would improve our understanding of atmosphere and ocean circulation, with possible consequences for weather prediction, and of fluid flows in engineering applications, such as the design of faster and more economically operated ships, planes, and vehicles.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
0608494
Program Officer
Michael H. Steuerwalt
Project Start
Project End
Budget Start
2006-07-01
Budget End
2010-06-30
Support Year
Fiscal Year
2006
Total Cost
$115,602
Indirect Cost
Name
University of Wyoming
Department
Type
DUNS #
City
Laramie
State
WY
Country
United States
Zip Code
82071