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Author(s):
K. Araki, S. Yanase and J. Mizushima
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Title:
Symmetry Breaking by Differential Rotation and Saddle-node Bifurcation of the Thermal Convection in a Spherical Shell
Date of publication:
Dec. 1995
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Key words:
thermal convection, spherical shell, saddle-node bifurcation, symmetry breaking by differential rotation.
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Abstract:
The effect of a weak azimuthal shear flow on the Benard 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.
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