### 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 Ra_{c}=Ra_{c}^{(0)}[1+(1-(3/2)λ_{G}) R^{-1}]+O(R^{-2}), where λ_{G} 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 language | English |
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Pages (from-to) | 2123-2132 |

Number of pages | 10 |

Journal | Journal of the Physical Society of Japan |

Volume | 63 |

Issue number | 6 |

Publication status | Published - Jun 1994 |

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### Keywords

- Bénard convection
- Spherical shell
- Thin layer approximation

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*63*(6), 2123-2132.

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

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 63, no. 6, pp. 2123-2132.

}

TY - JOUR

T1 - Thermal instability of a fluid in a spherical shell with thin layer approximation analysis

AU - Araki, Keisuke

AU - Mizushima, Jiro

AU - Yanase, Shinichiro

PY - 1994/6

Y1 - 1994/6

N2 - 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.

AB - 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.

KW - Bénard convection

KW - Spherical shell

KW - Thin layer approximation

UR - http://www.scopus.com/inward/record.url?scp=21844516176&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844516176&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:21844516176

VL - 63

SP - 2123

EP - 2132

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 6

ER -