Thermal instability of a fluid in a spherical shell with thin layer approximation analysis

Keisuke Araki, Jiro Mizushima, Shinichiro Yanase

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The thermal instability of a fluid layer confined in a spherical shell is investigated on a linear theory basis. The dependence of the critical Rayleigh number on the functional form of the gravity distribution is investigated. An asymptotic analysis is also made for very thin layer case by an expansion with R-1, where R is the radius of the inner sphere normalized by the thickness of the fluid layer. The critical Rayleigh number is obtained as Rac=Rac(0)[1+(1-(3/2)λG) R-1]+O(R-2), where λG is the density ratio of the fluid to the matter inside the inner sphere. The asymptotic expression of the Rayleigh number is shown to be a good approximation even for R of order one.

Original languageEnglish
Pages (from-to)2123-2132
Number of pages10
JournalJournal of the Physical Society of Japan
Volume63
Issue number6
Publication statusPublished - Jun 1994

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thermal instability
spherical shells
Rayleigh number
fluids
approximation
gravitation
radii
expansion

Keywords

  • Bénard convection
  • Spherical shell
  • Thin layer approximation

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Thermal instability of a fluid in a spherical shell with thin layer approximation analysis. / Araki, Keisuke; Mizushima, Jiro; Yanase, Shinichiro.

In: Journal of the Physical Society of Japan, Vol. 63, No. 6, 06.1994, p. 2123-2132.

Research output: Contribution to journalArticle

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