Large-Eddy Simulations: Where Are We and What Can We Expect?

Recent subgrid models for large-eddy simulations of turbulent flows are evaluated, particularly the dynamic-Smagorinsky combination, with emphasis on identifying the reasons for their success and the limits of their applicability. The argument is made that they reproduce the turbulent dissipation relatively well, but their main advantage is that they are robust to errors in that they have a built-in mechanism to adjust the dissipation without substantially modifying the larger scales. The question of the stresses is considered next. It is found that it is an intrinsic property of subgrid models that the stresses are essentially unpredictable, and the models considered are indeed found not to reproduce them correctly, even on the average. In particular, the stress-strain correlation is low in real turbulence, and because eddy viscosity models assume that both are proportional, they always result in either the wrong energy spectrum or the wrong stresses. This is confirmed by simulations of shear flows, where it is shown that the error of the mean flow can only be made small if the subgrid stresses are negligible. Stresses are however large-scale quantities that are carried by the resolved scales if the resolution is fine enough