where gi is the gravitational acceleration and the last approximation is applicable for small Froude numbers. Applying a gradient-diffusion modeling approach, Equation 4-157 can be recast into,

where σT is the turbulent Schmidt number. The production term in the ε equation is derived from the production term in the k equation. Hence, the corresponding term in the ε equation becomes,

where θ is the angle between u and g, accounting for the difference between buoyant vertical shear layers and buoyant horizontal shear layers. Using the relation between k, ε, and ω, the buoyancy production term in the w equation can be derived as,

The expressions for the various ε based and ω based turbulence models differ only in terms of constants and damping functions. Note that the v2-f turbulence model uses the wall distance to determine the relation between the wall-normal turbulent fluctuations and the acceleration of gravity. When the buoyancy contribution is determined from a multiphysics node, density variations with respect to the variable in the coupled physics interface are considered. For example, in nonisothermal flow the coupled interface is a Heat Transfer in Fluids interface, and, Equation 4-158 is replaced by,