Download PDF by M. Lesieur (auth.), Olivier Métais, Joel H. Ferziger (eds.): New Tools in Turbulence Modelling: Les Houches School, May

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Additional info for New Tools in Turbulence Modelling: Les Houches School, May 21–31, 1996

Sample text

Suppose we want to do large eddy simulations with the cutoff filter, the natural one for application to theories. We can ask how much energy is transferred from a given resolved wavenumber k to wavenumbers beyond the cutoff. If we call this energy transfer rate T>(k), we can define an effective spectral eddy viscosity: (10) Such an eddy viscosity was given by Lesieur [19]. There is a decrease in 1/7' at low wave-numbers that is of little consequence. The rise at the high wavenumbers is due to the nature of the interactions.

Long, thin regions of low speed fluid (streaks) are created. Resolving them requires a highly anisotropic grid and the length scale to be used in the SGS model is not obvious. In stably stratified flow, the Smagorinsky model parameter becomes a function of the Richardson number, a non-dimensional parameter that represents the relative importance of stratification and shear. Similar effects occur in flows with rotation and/or curvature. Thus, there are many difficulties with the Smagorinsky model.

X. In the zeal to include as much energy as possible, many authors ignore this point. Also, the subgrid scale model and numerical method need to be related. Piomelli et al. [11] showed that, with finite difference methods, the mixed model is best, while spectral LES is best carried out with the Smagorinsky model. The methods and step sizes in time and space should be chosen so that their errors are as nearly equal as possible. Accuracy is difficult to measure in DNS and LES. The reason is inherent in the nature of turbulent flows.

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