Large Eddy Numerical Simulations of Turbulent Flows

Large eddy simulations are a numerical technique in which large-scale turbulent structures are computed explicitly, and the small structures are modeled. Arguments for believing this method to be superior to more conventional approaches are given, the basis of the method is given, and some typical results displayed. The results show that the method does have enormous promise, but much further development is required. I. Rationale T URBULENCE originates in instabilities of laminar flow, the precise nature of which depend on the geometry of the flow. Generally, the instabilities produce wavelike structures which can absorb energy from the mean flow. As they grow, nonlinear effects cause energy transfers to other modes, and, eventually, the noisy pattern that is generally regarded as results. Fully developed turbulence always reflects its origins to some degree. Since the maintenance of turbulence requires continuous nourishment, turbulent structures must be capable of absorbing energy from the mean flow. Although the mean flow is changed by the presence of turbulence, the energy absorbing structures bear some resemblance to those from which the turbulence originated. Thus, in turbulent flows, the large structures are the ones which absorb energy from the mean flow. They tend to be highly anisotropic, vortical in nature, and quite variable from flow to flow, and they are responsible for most of the property transport in turbulent flows. Furthermore, since the production mechanism is largely the stretching of vortices, which is a process requiring three dimensions, we would argue that all true turbulent flows are three dimensional. Through nonlinear interactions, they transfer some of their energy to smaller-scale structures, and the major function of the small structures is to dissipate the energy provided by the larger ones. In contrast, it is well known that the parameters of the small scales are determined almost entirely by the amount of energy they are required to dissipate. For this reason, they are much more universal than the large structures, and they are therefore nearly the same in all flows and nearly isotropic. Over the past 10 to 20 years, a large body of experimental evidence for the picture just presented has been accumulating. The total picture is, in fact, much more complicated than that described in the foregoing, and it is likely to be some time before many of the missing elements are filled in. Almost all of the approaches to the prediction of turbulent flow are based on Reynolds' idea of averaging the NavierStokes equations over an ensemble of identical flows or some equivalent (time or span averaging) to obtain an equation for the mean velocity. The equations are not closed because of the nonlinear terms in the Navier-Stokes equations, so approximations are needed, i.e., models must be introduced. Since many of the difficulties that occur in this approach have analogs in what we will be doing in this paper, no direct discussion of them will be given here. Rather, the interested reader is referred to the recent review of these methods by Reynolds.1