Abstract
•This manuscript proposes a new layered structure of turbulent hydrodynamic and thermal layers for buoyant flow along a vertical plate.•A scaling patch approach is applied to quantify the layered structures.•The hydrodynamic layers are best subdivided into two layers.•Thermal layers are best subdivided into four layers.•The proposed approach results in excellent agreement with prior literature.
The layered structure of turbulent natural convection over a vertical flat plate (TNCVP) is first investigated qualitatively by dimensional analysis. The scaling patch approach is then applied to quantify the layered structure of TNCVP based on the characteristics of the mean momentum and energy equations. Fluid flow in TNCVP is divided into two layers: an inner layer and an outer layer, but heat transport is divided into four layers: a molecular diffusion sub-layer, a gradient balance layer, a meso layer and an outer layer. Scaling patch analysis identifies proper scales for the length, velocity, temperature, Reynolds shear stress, and turbulent heat flux in different layers, and develops a multi-scaling of the mean momentum and energy equations. Part of the novelty of the approach is that different regions incorporate unique scaling lengths, temperatures, turbulence temperature flux, and Reynolds stresses. The inner and outer scaled mean velocity, temperature, Reynolds shear stress and turbulent temperature flux profiles at four streamwise locations in the experiments of Tsuji and Nagano [1,2] merge onto a single curve in the inner and outer layers, respectively. This behavior supports the validity of the analysis. The layered structure of TNCVP is compared with three canonical turbulent flows: differentially heated turbulent flow in a vertical channel (DHVC), forced convection in turbulent boundary layer flows (TBL), and turbulent plumes. Striking similarities and distinctive differences among these turbulent flow and heat transport situations are elucidated. The inner layer of the mean momentum equation of TNCVP is similar to the inner layer of DHVC, but the outer layer of TNCVP is similar to that of a turbulent planar plume. The four layer structure for the mean energy equation of TNCVP is similar to that of pressure- or shear-driven turbulent boundary layers.