Analysis of mean momentum flux in subgrid models of turbulence

Abstract

Using a recently proposed model spectrum for weakly sheared turbulence [M. Ishihara, K. Yoshida, and Y. Kaneda, Phys. Rev. Lett. 88, 154501 (2002)], the mean momentum fluxes caused by subgrid scales are evaluated analytically. Using the result to calibrate the Smagorinsky coefficient, the value obtained is remarkably close to the traditional result obtained from balancing kinetic energy dissipation. For the Gaussian filter, the same conclusion is obtained when the Smagorinsky model is supplemented with the nonlinear model. It is concluded that when in practice the Smagorinsky model does not correctly predict the mean subgrid scale (SGS) stresses in large eddy simulation (LES), it must be due to either nonuniversal effects at large scales, or due to strong shear that violates the model spectrum assumed in the present analysis. Analysis of a two-parameter mixed model shows that the nonlinear term must be weighted more strongly in high shear conditions than in weak shear. © 2004 American Institute of Physics.