may be thought of as an effective turbulent viscosity. In fact, while much effort has been expended in developing good models for the Reynolds stress in a fluid, as a practical matter, when solving the fluid equations using computational fluid dynamics, often the simplest turbulence models prove the most effective. One class of models, closely related to the concept of turbulent viscosity, are the k-epsilon turbulence models, based upon coupled transport equations for the turbulent energy density (similar to the turbulent pressure, i.e. the trace of the Reynolds stress) and the turbulent dissipation rate . Typically, the average is formally defined as an ensemble average as in statistical ensemble theory. However, as a practical matter, the average may also be thought of as a spatial average over some length scale, or a temporal average. Note that, while formally the connection between such averages is justified in equilibrium statistical mechanics by the ergodic theorem, the statistical mechanics of hydrodynamic turbulence is currently far from understood. In fact, the Reynolds stress at any given point in a turbulent fluid is somewhat subject to interpretation, depending upon how one defines the average. References Turbulence Tensors