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Author(s):
K. Araki, J. Mizushima and S. Yanase
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Title:
The Non-axisymmetric Instability of the Wide-Gap Spherical Couette Flow
Date of publication:
Oct. 1996
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Key words:
spherical Couette flow, linear stability, supercritical Hopf bifurcation, spiral structure of the disturbance
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Abstract:
The non-axisymmetric linear stability of the spherical Couette flow is investigated numerically when the ratio of gap width to inner sphere radius (R_2 - R_1)/R_1= 0.5. The basic flow becomes unstable at Re_c = 1245 and the associated azimuthal wavenumber is n_c= 5, which agrees excellently with the experimental results by Egbers and Rath [Acta Mech. 81 (1990) pp.3-38]. The marginal mode is oscillatory and has the distinct wavy structure around the equator and the spiral structures extended in each hemisphere. Sufficiently large spatial resolution is found to be required in order to avoid a spuriously unstable eigenvalue that causes serious underestimation of the critical Reynolds number.
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