Linear eddy viscosity models
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.