The numerical computation of turbulence

This chapter deals primarily with the numerical computation of three-dimensional Navier-Stokes incompressible turbulence. As such, it leaves a lot of ground uncovered. It will be made clear early in the chapter that turbulence is not restricted to such flows, or even only to fluids, but this is the most common case in industrial applications, and most engineering computational schemes have been developed for it. Even when compressibility is important for the flow as a whole, such as in transonic flight, it does not affect turbulence strongly, and most of what is said here can be used with minor modifications. More extreme departures, such as hypersonics, plasmas, or the strong stratification of many geophysical flows, require changes that would make much of the material in this chapter irrelevant, except perhaps for the direct numerical simulations discussed in closed integral 6.5.. It would make little sense, for example, to use current RANS or LES models for two-dimensional turbulence. This chapter has two parts. Sections closed integral 6.1. to closed integral 6.3. are a, quick review of classical turbulence theory, with the goal of establishing the tools to be used later, and specially of defining the relevant turbulent length scales. The second part, formed by sections closed integral 6.4. to closed integral 6.7., describe the three levels of detail at which turbulence is nowadays computed. It is difficult in such a limited space to do more than to familiarize the reader with the requirements of each technique, and with the results that can be expected from them. The final result should at least be to allow him or her to determine which method to use in a particular situation. A subject such as this cannot be discussed without some reference to numerical analysis, which is the tool of simulations. This is specially true in the case of turbulence, where the flow field is not smooth, and therefore not easy to represent numerically. Any reader seriously interested in computing turbulence should, of course, familiarize her or himself as much as possible with numerical techniques.