ONE-POINT CLOSURE MODELS FOR BUOYANCY-DRIVEN TURBULENT FLOWS

Turbulent flows driven by thermal buoyancy are featured by phenomena that pose a special challenge to conventional one-point closure models. Inherent unsteadiness, energy nonequilibrium, counter-gradient diffusion, strong pressure fluctuations, and lack of universal scaling, all believed to be associated with distinct large-scale coherent eddy structures, are hardly tractable by Reynolds-type averaging. Second-moment closures, though inadequate for providing information on eddy structure, offer better prospects than eddy-viscosity models for capturing at least some of the phenomena. For some configurations (e.g., with heating from below), unsteady computational solutions of ensemble-averaged equations, using a one-point closure as the subscale model, may be unavoidable for accurate prediction of flow details and wall heat transfer. This article reviews the rationale and some specific modeling issues related to buoyant flows within the realm of one-point closures. The inadequacy of isotropic eddy-diffusivity models is discussed first, followed by the rationale of the second-moment modeling and its term-by-term scrutiny based on direct numerical simulations (DNS). Algebraic models based on a rational truncation of the differential second-moment closure are proposed as the minimum closure level for complex flows. These closures are also recommended as subscale models for transient statistical modeling (T-RANS) and very large eddy simulations (VLES). Examples of applications illustrate some recent achievements.