### Abstract

The effect of a weak azimuthal shear flow on the Bénard convection in a spherical shell is investigated numerically where gravity is directed to the center of the spheres. Differential rotation of the spheres is introduced as the simplest driving mechanism of the shear flow. Axisymmetric steady solutions are obtained by an iterative method and their stability is analyzed. Bifurcation diagram of the steady solutions is extensively searched over the parameter space. It is shown by both the fully numerical calculation and the weakly nonlinear analysis that the weak shear flow breaks the asymptotic reflection symmetry due to the self-adjointness of the linearized system so that the pitchfork bifurcation is deformed and the saddle-node bifurcation occurs.

Original language | English |
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Pages (from-to) | 3862-3870 |

Number of pages | 9 |

Journal | journal of the physical society of japan |

Volume | 65 |

Issue number | 12 |

DOIs | |

Publication status | Published - Jan 1 1996 |

### Keywords

- Saddle-node bifurcation
- Spherical shell
- Symmetry breaking by differential rotation
- Thermal convection

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*journal of the physical society of japan*,

*65*(12), 3862-3870. https://doi.org/10.1143/JPSJ.65.3862