### Abstract

Linear stability of rotating thermal convection in a horizontal layer of Boussinesq fluid under the fixed heat flux boundary condition is examined by the use of a vertically truncated system up to wavenumber one. When the rotation axis is in the vertical direction, the asymptotic behavior of the critical convection for large rotation rates is almost the same as that under the fixed temperature boundary condition. However, when the rotation axis is horizontal and the lateral boundaries are inclined, the mode with zero horizontal wavenumber remains as the critical mode regardless of the rotation rate. The neutral curve has another local minimum at a nonzero horizontal wavenumber, whose asymptotic behavior coincides with the critical mode under the fixed temperature condition. The difference of the critical horizontal wavenumber between those two geometries is qualitatively understood by the difference of wave characteristics; inertial waves and Rossby waves, respectively.

Original language | English |
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Pages (from-to) | 439-459 |

Number of pages | 21 |

Journal | Geophysical and Astrophysical Fluid Dynamics |

Volume | 96 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 1 2002 |

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### All Science Journal Classification (ASJC) codes

- Geochemistry and Petrology
- Geophysics
- Mechanics of Materials
- Computational Mechanics
- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Geophysical and Astrophysical Fluid Dynamics*,

*96*(6), 439-459. https://doi.org/10.1080/0309192021000036996

**Linear stability of thermal convection in rotating systems with fixed heat flux boundaries.** / Takehiro, Shin Ichi; Ishiwatari, Masaki; Nakajima, Kensuke; Hayashi, Yoshi Yuki.

Research output: Contribution to journal › Article

*Geophysical and Astrophysical Fluid Dynamics*, vol. 96, no. 6, pp. 439-459. https://doi.org/10.1080/0309192021000036996

}

TY - JOUR

T1 - Linear stability of thermal convection in rotating systems with fixed heat flux boundaries

AU - Takehiro, Shin Ichi

AU - Ishiwatari, Masaki

AU - Nakajima, Kensuke

AU - Hayashi, Yoshi Yuki

PY - 2002/12/1

Y1 - 2002/12/1

N2 - Linear stability of rotating thermal convection in a horizontal layer of Boussinesq fluid under the fixed heat flux boundary condition is examined by the use of a vertically truncated system up to wavenumber one. When the rotation axis is in the vertical direction, the asymptotic behavior of the critical convection for large rotation rates is almost the same as that under the fixed temperature boundary condition. However, when the rotation axis is horizontal and the lateral boundaries are inclined, the mode with zero horizontal wavenumber remains as the critical mode regardless of the rotation rate. The neutral curve has another local minimum at a nonzero horizontal wavenumber, whose asymptotic behavior coincides with the critical mode under the fixed temperature condition. The difference of the critical horizontal wavenumber between those two geometries is qualitatively understood by the difference of wave characteristics; inertial waves and Rossby waves, respectively.

AB - Linear stability of rotating thermal convection in a horizontal layer of Boussinesq fluid under the fixed heat flux boundary condition is examined by the use of a vertically truncated system up to wavenumber one. When the rotation axis is in the vertical direction, the asymptotic behavior of the critical convection for large rotation rates is almost the same as that under the fixed temperature boundary condition. However, when the rotation axis is horizontal and the lateral boundaries are inclined, the mode with zero horizontal wavenumber remains as the critical mode regardless of the rotation rate. The neutral curve has another local minimum at a nonzero horizontal wavenumber, whose asymptotic behavior coincides with the critical mode under the fixed temperature condition. The difference of the critical horizontal wavenumber between those two geometries is qualitatively understood by the difference of wave characteristics; inertial waves and Rossby waves, respectively.

UR - http://www.scopus.com/inward/record.url?scp=33747730864&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747730864&partnerID=8YFLogxK

U2 - 10.1080/0309192021000036996

DO - 10.1080/0309192021000036996

M3 - Article

AN - SCOPUS:33747730864

VL - 96

SP - 439

EP - 459

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

SN - 0309-1929

IS - 6

ER -