Large Rayleigh number thermal convection: Heat flux predictions and strongly nonlinear solutions

• Published in: Physics of fluids (1994) Vol. 21; no. 8
• Main Authors: CHINI, Gregory P, COX, Stephen M
• Format: Journal Article
• Language: English
• Published: Melville, NY American Institute of Physics 01.08.2009
• Subjects: Buoyancy-driven instability; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Physics; Matched asymptotic expansion; Rayleigh-Benard instability; Convective instabilities; Cellular convection; Integral equations; Digital simulation; Boundary conditions; Modelling; Boundary layers; Plumes; Heat transfer
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.3210777

We investigate the structure of strongly nonlinear Rayleigh–Bénard convection cells in the asymptotic limit of large Rayleigh number and fixed, moderate Prandtl number. Unlike the flows analyzed in prior theoretical studies of infinite Prandtl number convection, our cellular solutions exhibit dynamically inviscid constant-vorticity cores. By solving an integral equation for the cell-edge temperature distribution, we are able to predict, as a function of cell aspect ratio, the value of the core vorticity, details of the flow within the thin boundary layers and rising/falling plumes adjacent to the edges of the convection cell, and, in particular, the bulk heat flux through the layer. The results of our asymptotic analysis are corroborated using full pseudospectral numerical simulations and confirm that the heat flux is maximized for convection cells that are roughly square in cross section.