Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows

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Numerical simulation of all the scales of a turbulent flow, even at modest Reynolds numbers, is generally not practical; however, most information of interest can be obtained by simulating the motion of the large-scale, energy containing eddies. This chapter describes the derivation of smoothed or filtered momentum, and the continuity equations for large-scale energy containing eddies. The large-scale fluctuations satisfy the filtered or averaged momentum and continuity equations. Averaging the nonlinear advection term yields two terms; one is the Reynolds stress contribution from the subgrid-scale turbulence, and the other is the filtered advection term for the large scales. In some models, the energy cascade is viewed solely as an energy loss of the large-scales because of an artificial viscosity arising from subgrid-scale motions. However, in most cases of interest, motions on the order of the dissipation length scale cannot be treated explicitly, and modifications of the Navier-Stokes equations must be introduced to simulate properly the energy cascade. Noting that the large-scale motions vary in a nonnegligible way over an averaging volume, the chapter investigates a more accurate, modified advective term in the momentum equations for these motions.

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Present address: NASA Ames Research Center, Moffett Field, California 94035, U.S.A.

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