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Interpretation of shadowgraph patterns in Rayleigh-Bénard convection

Published online by Cambridge University Press:  21 April 2006

D. R. Jenkins
D. R. Jenkins
Affiliation:
CSIRO Division of Mathematics and Statistics, PO Box 218, Lindfield NSW 2070, Australia
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Abstract

The relationship between observations of cellular Rayleigh-Bénard convection using shadowgraphs and theoretical expressions for convection planforms is considered. We determine the shadowgraphs that ought to be observed if the convection is as given by theoretical expressions for roll, square or hexagonal planforms and compare them with actual experiments. Expressions for the planforms derived from linear theory, valid for low supercritical Rayleigh number, produce unambiguous shadowgraphs consisting of cells bounded by bright lines, which correspond to surfaces through which no fluid flows and on which the vertical component of velocity is directed downwards. Dark spots at the centre of cells, indicating regions of hot, rising fluid, are not accounted for by linear theory, but can be produced by adding higher-order terms, predominantly due to the temperature dependence of a material property of the fluid, such as its viscosity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 190 , May 1988 , pp. 451 - 469
Copyright
© 1988 Cambridge University Press

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