The effects of buoyancy can be included in the transport equations of the turbulence kinetic energy k (Equation 4–71, Equation 4–101) and the specific dissipation rate (Equation 4–72, Equation 4–102).

The turbulence generation due to buoyancy () is modeled in the same way as for the turbulence models based on the transport equation of the dissipation rate (see Effects of Buoyancy on Turbulence in the k-ε Models). It is by default included in the transport equation of the turbulence kinetic energy k.

The buoyancy term in the -equation () is derived from the k and equations (Equation 4–39 and Equation 4–40) using the following relations:

(4–127)

(4–128)

This derivation leads to the following transformation of the buoyancy source terms:

(4–129)

The first part of the buoyancy term from the equation, , comes from the transport equation of the dissipation rate. The model coefficient, , is replaced with , where is the corresponding coefficient of the production term in the -equation. In the BSL and SST model, this coefficient is a linear combination of the corresponding coefficients of the - and the transformed k-ε models. For the k-ε model, the value of is 0.44. The value of in the standard k-ε model is recovered from this value of .

The coefficient is not specified, but is instead calculated according to Equation 4–67.

The final formulation of the buoyancy source terms for the -transport equation thus reads:

(4–130)

The second part is included by default, whereas the first part is only included if the full buoyancy model is specified in the Viscous Models dialog box (see Including Buoyancy Effects on Turbulence in the Fluent User's Guide).