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

By Gregory P. Chini and Stephen M. Cox

Abstract

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

Publisher: American Institute of Physics
Year: 2009
OAI identifier: oai:eprints.nottingham.ac.uk:1258
Provided by: Nottingham ePrints

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