# Linear eddy viscosity models

(Difference between revisions)
 Revision as of 17:13, 30 October 2009 (view source)← Older edit Revision as of 17:14, 30 October 2009 (view source)Newer edit → Line 1: Line 1: - These are turbulence models in which the [[Introduction to turbulence/Reynolds averaged equations|Reynolds stresses]] 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: :[itex] :[itex]

## Revision as of 17:14, 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:

$- \rho \left\langle u_{i} u_{j} \right\rangle = \mu_{t} \left[ S_{ij} - \frac{1}{3} S_{kk} \delta_{ij} \right]$

where $\mu_{t}$ is the coefficient termed turbulence "viscosity" (also called the eddy viscosity), and $S_{ij}$ is the mean strain rate defined by:

$S_{ij}= \frac{1}{2} \left[ \frac{\partial U_{i}}{\partial x_{j}} + \frac{\partial U_{j}}{\partial x_{i}} \right]$

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.