Angular distribution of turbulence in wave space

As experience with the one-point closure models for turbulence in current use has not been completely satisfactory, people have begun to search for other ways to predict turbulent flows. One alternative that has been suggested is large eddy simulation (LES) which, together with its more exact relative, direct numerical simulation (DNS), has had considerable success in the prediction of turbulent flows. These methods are beginning to serve as partial substitutes for turbulence experiments. It is perhaps natural that people should regard these new methods as panaceas. More careful consideration will lead one to be more cautious. DNS and LES have been applied only to the simplest low Reynolds number turbulent flows. The prospects for a large increase in the range of applicability of DNS in the near future are very small. For LES, the prospects are somewhat brighter. The range of flows that has been treated with LES to date is only a little broader than that treated by DNS. The Reynolds numbers are somewhat higher but the geometries are almost as restricted. Three items pace the growth of LES applications. The first is computational resources: speed, memory (both fast and archival), and number of processors available. The second is numerical methods; there is, and perhaps always will be, a need for faster algorithms applicable to a wide range of geometries. Finally, there are the subgrid models required by LES; this is the focus of the present work. In simulations done to date, the Reynolds numbers were such that most of the turbulence energy resided in the resolved scales. Under these circumstances, the results are relatively insensitive to the quality of the model used for the subgrid scale (SGS) component of the turbulence. As one pushes LES to higher Reynolds numbers or more complex flows, the model quality becomes a more important issue. It is safe to say that, if the models in current use are applied to these more difficult flows, the results will be of reduced quality. Thus the development of improved SGS models must be of highest priority if LES is to become an engineering tool. SGS models in current use are, for the most part, based on the same ideas as onepoint closure models. To obtain significant improvements, new ideas will probably be needed. It is here that turbulence theories may have a role to play.