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  .