Buoyancy-Driven Flows—Beyond the Boussinesq Approximation

Buoyancy-driven flows are analyzed to determine the limits of applicability of the Boussinesq approximation. Alternative approaches are derived and tested for flows with high Richardson numbers. A generalized treatment is proposed for the effect of buoyancy on turbulence, which can be either stabilizing or destabilizing based on orientation relative to the gravity vector. Results are validated with three test problems with strong buoyancy effects, and with significant directional turbulence effects on mixing.