# Linear eddy viscosity models

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- | These are turbulence models in which the [[Introduction to turbulence/Reynolds averaged equations|Reynolds stresses]] as obtained from a [[Introduction to turbulence/Reynolds averaged equations|Reynolds averaging of the Navier-Stokes equations]] are modelled by a ''linear constitutive relationship'' with the ''mean'' flow straining field, such as: | + | These are turbulence models in which the [[Introduction to turbulence/Reynolds averaged equations|Reynolds stresses]], as obtained from a [[Introduction to turbulence/Reynolds averaged equations|Reynolds averaging of the Navier-Stokes equations]], are modelled by a ''linear constitutive relationship'' with the ''mean'' flow straining field, such as: |

:<math> | :<math> |

## Revision as of 22:28, 30 October 2009

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, such as:

where is the coefficient termed turbulence "viscosity" (also called the eddy viscosity), and is the *mean* strain rate defined by:

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 are solved for to compute the eddy viscosity coefficient.