The PDEs known as the Euler and Navier-Stokes equations are the most important deterministic models for the motion of fluids and gases. It has long been suspected that stochastic versions of Navier-Stokes or Euler equations could be valuable models for turbulent motion. The research to be performed is concerned with developing methods for specifying stochastic versions of equations of fluid dynamics related to turbulence, investigating their properties, and constructing numerical approximations and asymptotics.
Turbulence is prominent in numerous contexts of significance for science and technology, including oceanography, climatology, flight dynamics, navigation, combustion and propulsion, etc. The proposed research deals with mathematical models of turbulence that capture its essential behavior, and also yield computationally tractable representations. Related numerical algorithms will be developed, coded, and tested.
