In Chapter 6 we discussed the fundamentals of turbulence and reviewed the mixing length and eddy diffusivity models. As was mentioned there, these classical models do not treat turbulence as a transported property, and as a result they are best applicable to equilibrium turbulent fields. In an equilibrium turbulent field at any particular location there is a balance among the generation, dissipation, and transported turbulent energy for the entire eddy size spectrum, and as a result turbulence characteristics at each point only depend on the local parameters at that point.

Our daily experience, however, shows that turbulence is in general a transported property, and turbulence generated at one location in a flow field affects the flow field downstream from that location. One can see this by simply disturbing the surface of a stream and noting that the vortices resulting from the disturbance move downstream.

In this chapter, turbulence models that treat turbulence as a transported property are discussed. Turbulence models based on Reynolds–averaged Navier–Stokes [(RANS)-type] models are first discussed. These models, as their title suggests, avoid the difficulty of dealing with turbulent fluctuations entirely. We then discuss two methods that actually attempt to resolve these turbulent fluctuations, either over the entire range of eddy sizes [direct numerical simulation (DNS) method] or over the range of eddies that are large enough to have nonuniversal behavior [largeeddy simulation (LES) method].