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### From CFD-Wiki

foo bar (I am trying to see how this text introduction works) Turbulence Theory Munson et al. (1994) define turbulence as a characteristic of a flow pattern that is random in nature; in other words there is no regular variation or repeatable sequence of the unsteadiness. In fluid motion, this means that local velocities and pressure fluctuate irregularly. Turbulence can be regarded as a highly disordered motion resulting from the growth of instabilities in the flow. Most engineering designs are concerned with turbulence time-averaged effects, even when the mean flow is unsteady. This process of time-averaging the equations of motion (Navier Stokes’ equations) creates statistical correlations that incorporate fluctuating velocities (and other transport properties) in the conservation equations. The resultant set of equations solved for the problem are the Reynolds Averaged Navier-Stokes (RANS) equations (Fluent, 1999) of turbulence. Thus, the RANS consists of partial differential equations that provide local information to the model, as well as accuracy, and a rather general applicability to the problem.

Since there is no direct measuring method for the magnitude of the statistical correlations that are due to the time-averaging process, a model to approximate these terms or quantities is needed. This approximation is commonly called the model of turbulence. The approximation is a set of additional equations which, when solved with the mean-flow equations (RANS), permits the computation of the appropriate correlations (fluctuating velocities) which allow the analyst to perform simulations on the behavior of real fluids.

THE TURBULENT VISCOSITY CONCEPT

Over a century ago, Boussinesq suggested that effective turbulent shear stress (Rij), arising from the cross-correlation of fluctuating velocities, could be replaced by the product of the mean velocity gradient and a quantity termed the turbulent viscosity, (mu-t), (Garde, 1994). The turbulent viscosity supplies the structure to build a turbulent model. The turbulent viscosity is not a property of the fluid, and thus its value is mostly determined by the local structure of turbulence, at a place or point under analysis in the flow domain. In many circumstances, two properties, the local velocity and the length scale of the turbulence can adequately define the local structure of turbulence