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Large-Eddy Simulations of Turbulent Flows

Student-Run Research Seminar

Speaker: Branko Kosovic, University of California at Davis Department of Mathematics
Location: 693 Kerr
Start time: Mon, Nov 6 2000, 11:00AM

Despite the fact that the question about the existence of smooth solutions to Naiver-Stokes equations in three dimensions for all times remains open numerical simulations of fluid flows based on these equations are carried out regularly because of their great importance in a wide range of applications. However, when attempting to numerically simulate turbulent flows (flows at high Reynolds numbers) we are faced with, so called, ''turbulence closure problem.'' The turbulence closure problem is a direct consequence of the fact that a solution to a nonlinear, infinite dimensional space problem is sought by using some numerical scheme on a finite mesh. The closure is achieved by assuming that small turbulent eddies, which cannot be resolved numerically, are enslaved by large eddies. Then, the effect of small eddies on the evolution of large ones can be parameterized using only large features of the flow. This approach forms the foundations of large-eddy simulations, in engineering and atmospheric sciences. Some examples of phenomenological parameterizations used to obtain the turbulence closure will be presented and compared to the recently derived Lagrangian Averaged Navier-Stokes equations. Lagrangian Averaged Navier-Stokes equations represent a promising novel approach to the closure problem that does not depend on {it ad +hoc} assumptions commonly used in large-eddy simulations.