A simple analytic approximation to the Rayleigh-B ?enard stability threshold
Date
12/7/2011
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
The Physics of Fluids
Abstract
The Rayleigh-Bénard linear stability problem is solved by means of a Fourier series expansion. It is found that truncating the series to just the first term gives an excellent explicit approximation to the marginal stability relation between the Rayleigh number and the wave number of the perturbation. Where the error can be compared with published exact results, it is found not to exceed a few percent over the entire wave number range. Several cases with no-slip boundaries of equal or unequal thermal conductivities are considered explicitly.
Description
Keywords
Control theory, Thermal diffusion, Linear stability analysis, Fourier analysis, Porous media, Matrix calculus
Citation
Copyright 2011 Physics of Fluids. Recommended citation: Prosperetti, Andrea. "A simple analytic approximation to the Rayleigh-Bénard stability threshold." Physics of fluids 23, no. 12 (2011): 124101. DOI: 10.1063/1.3662466 URL: https://aip.scitation.org/doi/abs/10.1063/1.3662466 Reproduced in accordance with the original publisher’s licensing terms and with permission from the author(s).