A simple analytic approximation to the Rayleigh-Bénard stability threshold

Andrea Prosperetti

doi:10.1063/1.3662466

A simple analytic approximation to the Rayleigh-Bénard stability threshold

Andrea Prosperetti

Physics of Fluids

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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

Original language	English
Pages (from-to)	124101-1-124101-8
Number of pages	8
Journal	Physics of fluids
Volume	23
Issue number	12
DOIs	https://doi.org/10.1063/1.3662466
Publication status	Published - 2011

Keywords

METIS-281517
IR-78762

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10.1063/1.3662466

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http://pof.aip.org/resource/1/phfle6/v23/i12/p124101_s1

Cite this

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title = "A simple analytic approximation to the Rayleigh-B{\'e}nard stability threshold",

abstract = "The Rayleigh-B{\'e}nard 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",

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AU - Prosperetti, Andrea

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N2 - 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

AB - 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

KW - METIS-281517

KW - IR-78762

U2 - 10.1063/1.3662466

DO - 10.1063/1.3662466

M3 - Article

SN - 1070-6631

VL - 23

SP - 124101-1-124101-8

JO - Physics of fluids

JF - Physics of fluids

IS - 12

ER -

A simple analytic approximation to the Rayleigh-Bénard stability threshold

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Keywords

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