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Modified Rayleigh-Bénard convection driven by long-wavelength heating from above and below


Floryan, JM and Hossain, MZ and Bassom, AP, Modified Rayleigh-Benard convection driven by long-wavelength heating from above and below, Theoretical and Computational Fluid Dynamics, 33, (1) pp. 37-57. ISSN 0935-4964 (2019) [Refereed Article]

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Copyright 2019 Springer-Verlag GmbH Germany, part of Springer Nature

DOI: doi:10.1007/s00162-018-0482-0


Classical Rayleigh-Benard convection occurs when a horizontal fluid layer is heated sufficiently strongly from below. In more recent times, there has been increased interest in structured convection, when the heating that is applied is no longer uniform but rather spatially varying in some way. Here, we examine the effect of structured convection in a fluid layer when both the lower and upper boundaries are heated so that their temperatures fluctuate sinusoidally over a common long length scale offset by some phase 𝛺 . While this non-uniform heating can be shown to induce small fluid motions by way of a primary form of convection, some previous computations have shown that the layer is also susceptible to a stronger, secondary form of convection. When the heating is just sufficient to induce this secondary motion, the cells tend to conglomerate near the local hot spots where the underlying heating is at its most intense. The strength of the secondary convection falls off away from the hot spot on a length scale which is appreciably longer than the wavelength of the individual cells but also much shorter than the wavelength of the underlying applied heating. In this work, we derive a second-order amplitude equation that describes the secondary convection and discuss the important features of its solution. These are compared with some direct numerical simulations and are likely to apply for other situations in which long-scale heating gives rise to structured convection patterns.

Item Details

Item Type:Refereed Article
Keywords:distributed heating, secondary flow, long wavelength modes, convection, long wavelength heating
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:130562
Year Published:2019
Web of Science® Times Cited:2
Deposited By:Mathematics and Physics
Deposited On:2019-02-04
Last Modified:2021-06-01

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