For RANS turbulence models and hybrid models (that is, Scale-Adaptive Simulation, Detached Eddy Simulation, and Shielded Detached Eddy Simulation), the velocity scales and are defined as:

(4–449)

(4–450)

where is the turbulence kinetic energy, is the dissipation rate, is the molecular viscosity, and is the density.

The time scales and are defined in the following way:

(4–451)

(4–452)

In turbulence models based on the -equation, the dissipation rate is calculated using the relation

(4–453)

where is a model coefficient.

Using Reynolds stress models, the turbulence kinetic energy is defined as the trace of the Reynolds stress tensor:

(4–454)