### Abstract

Two-dimensional thermal convection in a rotating cylindrical annulus under a fixed heat flux boundary condition is examined in order to consider the effects of thermal boundary condition on convection in rapidly rotating spherical shells. Nonlinear numerical calculations show the existence of a state where convection cells with a small horizontal scale are superimposed in cells with a large horizontal scale in the case of a constant coefficient of topographic β effect. However, when the effect of a spherical boundary is included, small scale cells in a large clockwise circulation disappear and they exists only in a large anti-clockwise circulation. Such asymmetric emergence of small scale cells is consistent with the expectation by Orr mechanism. The linear stability analyses of a three-dimensional system of rotating spherical shells also suggest the emergence of convection cells with a large horizontal scale under the fixed heat flux condition.

Original language | English |
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Pages (from-to) | 415-421 |

Number of pages | 7 |

Journal | Theoretical and Applied Mechanics |

Volume | 48 |

Publication status | Published - Dec 1 1999 |

Event | Proceedings of the 1999 48th Japan National Congress on Theoretical and Applied Mechanics (NCTAM) - Tokyo, Jpn Duration: Jan 25 1999 → Jan 27 1999 |

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### All Science Journal Classification (ASJC) codes

- Mechanics of Materials

### Cite this

*Theoretical and Applied Mechanics*,

*48*, 415-421.

**Effects of thermal boundary condition on convection in rapidly rotating spherical shells.** / Takehiro, Shin Ichi; Ishiwatari, Masaki; Nakajima, Kensuke; Hayashi, Yoshi Yuki.

Research output: Contribution to journal › Conference article

*Theoretical and Applied Mechanics*, vol. 48, pp. 415-421.

}

TY - JOUR

T1 - Effects of thermal boundary condition on convection in rapidly rotating spherical shells

AU - Takehiro, Shin Ichi

AU - Ishiwatari, Masaki

AU - Nakajima, Kensuke

AU - Hayashi, Yoshi Yuki

PY - 1999/12/1

Y1 - 1999/12/1

N2 - Two-dimensional thermal convection in a rotating cylindrical annulus under a fixed heat flux boundary condition is examined in order to consider the effects of thermal boundary condition on convection in rapidly rotating spherical shells. Nonlinear numerical calculations show the existence of a state where convection cells with a small horizontal scale are superimposed in cells with a large horizontal scale in the case of a constant coefficient of topographic β effect. However, when the effect of a spherical boundary is included, small scale cells in a large clockwise circulation disappear and they exists only in a large anti-clockwise circulation. Such asymmetric emergence of small scale cells is consistent with the expectation by Orr mechanism. The linear stability analyses of a three-dimensional system of rotating spherical shells also suggest the emergence of convection cells with a large horizontal scale under the fixed heat flux condition.

AB - Two-dimensional thermal convection in a rotating cylindrical annulus under a fixed heat flux boundary condition is examined in order to consider the effects of thermal boundary condition on convection in rapidly rotating spherical shells. Nonlinear numerical calculations show the existence of a state where convection cells with a small horizontal scale are superimposed in cells with a large horizontal scale in the case of a constant coefficient of topographic β effect. However, when the effect of a spherical boundary is included, small scale cells in a large clockwise circulation disappear and they exists only in a large anti-clockwise circulation. Such asymmetric emergence of small scale cells is consistent with the expectation by Orr mechanism. The linear stability analyses of a three-dimensional system of rotating spherical shells also suggest the emergence of convection cells with a large horizontal scale under the fixed heat flux condition.

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M3 - Conference article

AN - SCOPUS:0033308632

VL - 48

SP - 415

EP - 421

JO - Theoretical and Applied Mechanics

JF - Theoretical and Applied Mechanics

SN - 0285-6042

ER -