AMC-SS: 3D Stochastic Equations of Fluid Dynamics and Wiener Chaos

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The PDEs known as the Euler and Navier-Stokes equations are the most importantdeterministic models for the motion of fluids and gases. It has long beensuspected that stochastic versions of Navier-Stokes or Euler equations couldbe valuable models for turbulent motion. The research to be performed isconcerned with developing methods for specifying stochastic versions ofequations of fluid dynamics related to turbulence, investigating theirproperties, and constructing numerical approximations and asymptotics.Turbulence is prominent in numerous contexts of significance for science andtechnology, including oceanography, climatology, flight dynamics, navigation,combustion and propulsion, etc. The proposed research deals with mathematicalmodels of turbulence that capture its essential behavior, and also yieldcomputationally tractable representations. Related numerical algorithms willbe developed, coded, and tested.