# Linear eddy viscosity models

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- | :Note that that inclusion of <math>\frac{2}{3} \rho k \delta_{ij}</math> in the linear constitutive relation is required by tensorial algebra purposes when solving for [[Two equation models|two-equation turbulence models]] (or any other turbulence model that solves a transport | + | :Note that that inclusion of <math>\frac{2}{3} \rho k \delta_{ij}</math> in the linear constitutive relation is required by tensorial algebra purposes when solving for [[Two equation models|two-equation turbulence models]] (or any other turbulence model that solves a transport equation for <math>k</math>. |

## Latest revision as of 18:38, 7 June 2011

These are turbulence models in which the Reynolds stresses, as obtained from a Reynolds averaging of the Navier-Stokes equations, are modelled by a *linear constitutive relationship* with the *mean* flow straining field, as:

where

- is the coefficient termed turbulence "viscosity" (also called the eddy viscosity)
- is the mean turbulent kinetic energy
- is the
*mean*strain rate

- Note that that inclusion of in the linear constitutive relation is required by tensorial algebra purposes when solving for two-equation turbulence models (or any other turbulence model that solves a transport equation for .

This linear relationship is also known as *the Boussinesq hypothesis*. For a deep discussion on this linear constitutive relationship, check section Introduction to turbulence/Reynolds averaged equations.

There are several subcategories for the linear eddy-viscosity models, depending on the number of (transport) equations solved for to compute the eddy viscosity coefficient.