Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions
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 dynami...
| Main Authors: | , |
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| Format: | Article |
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American Institute of Physics
2009
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| Online Access: | https://eprints.nottingham.ac.uk/1258/ |
| _version_ | 1848790571309596672 |
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| author | Chini, Gregory P. Cox, Stephen M. |
| author_facet | Chini, Gregory P. Cox, Stephen M. |
| author_sort | Chini, Gregory P. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:14:44Z |
| format | Article |
| id | nottingham-1258 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:14:44Z |
| publishDate | 2009 |
| publisher | American Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-12582020-05-04T20:26:41Z https://eprints.nottingham.ac.uk/1258/ Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions Chini, Gregory P. Cox, Stephen M. 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. American Institute of Physics 2009 Article PeerReviewed Chini, Gregory P. and Cox, Stephen M. (2009) Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions. Physics of Fluids, 21 . 083603-1. ISSN 1070-6631 http://pof.aip.org/phfle6/v21/i8/p083603_s1 doi:10.1063/1.3210777 doi:10.1063/1.3210777 |
| spellingShingle | Chini, Gregory P. Cox, Stephen M. Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions |
| title | Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions |
| title_full | Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions |
| title_fullStr | Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions |
| title_full_unstemmed | Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions |
| title_short | Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions |
| title_sort | large rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions |
| url | https://eprints.nottingham.ac.uk/1258/ https://eprints.nottingham.ac.uk/1258/ https://eprints.nottingham.ac.uk/1258/ |