Symmetry Breaking by Differential Rotation and Saddle-Node Bifurcation of the Thermal Convection in a Spherical Shell

Keisuke Araki, Shinichiro Yanase, Jiro Mizushima

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)3862-3870
Number of pages9
Journaljournal of the physical society of japan
Volume65
Issue number12
DOIs
Publication statusPublished - 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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