Analyses of buoyancy-driven convection

Abstract

This article investigates the multilayer structure of turbulent flow and heat transport in buoyancy-driven convection, and in particular, introduces a relatively new scaling patch approach. A differentially heated vertical channel (DHVC) is used as an example of buoyancy-driven convection, and its multilayer structure is first qualitatively investigated by dimensional analysis. In the near-wall region of turbulent DHVC, flow and heat transport is strongly influenced by the molecular diffusion, and the kinematic viscosity and thermal diffusivity are important control parameters in the dimensional analysis. Flow and heat transport in the inner layer is controlled by two nondimensional numbers: the Prandtl number of the fluid and an inner Richardson number. Away from the wall, flow and heat transport are dominated by eddy motions, largely independent of molecular diffusion. The controlling nondimensional parameter in the outer layer of turbulent DHVC is an outer Richardson number. The multilayer structure in turbulent DHVC is then elucidated quantitatively by the scaling patch analysis. Based on the characteristics of force balance, the mean momentum equation is divided into three layers: an inner layer, a meso layer, and an outer layer. The inner and outer Richardson numbers, derived from the dimensional analysis, appear naturally in the properly scaled mean momentum equation. Another nondimensional number that appears naturally from the scaling patch analysis is the friction Reynolds number. The characteristic length scale in the inner layer is directly influenced by the friction Reynolds number, distinctively different from that in forced convection. The characteristic length scale in the meso layer is an Obukhov-style length scale. The mean heat equation can also be divided into multiple layers. In fact, an inherent hierarchy of layer structure (scaling patches) is revealed through a simple transformation of the turbulent temperature flux. A new prediction of the Nusselt number is developed based on the insight gained from the dimensional analysis and scaling patch analysis. The new prediction is directly connected to the multilayer structure of heat transport in turbulent DHVC and is fundamentally different from the traditional power-law correlations.