The nonaxisymmetric instability of the wide-gap spherical Couette flow

Keisuke Araki; Jiro Mizushima; Shinichiro Yanase

doi:10.1063/1.869177

The nonaxisymmetric instability of the wide-gap spherical Couette flow

Keisuke Araki, Jiro Mizushima, Shinichiro Yanase

Graduate School of Natural Science and Technology

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

The nonaxisymmetric linear stability of spherical Couette flow is investigated numerically when the ratio of gap width to inner sphere radius (R₂ - R₁)/R₁ = 0.5. The basic flow becomes unstable at Re_c = 1245 and the associated azimuthal wave number is n_c = 5, which agrees remarkably well with the experimental results by Egbers and Rath [Acta Mech. 81, 3 (1990)]. The marginal mode is oscillatory and has a distinctive wavy structure around the equator and spirals extended in each hemisphere. Sufficiently large spatial resolution is found to be required in order to avoid serious underestimation of the critical Reynolds number.

Original language	English
Pages (from-to)	1197-1199
Number of pages	3
Journal	Physics of Fluids
Volume	9
Issue number	4
DOIs	https://doi.org/10.1063/1.869177
Publication status	Published - Apr 1997

ASJC Scopus subject areas

Computational Mechanics
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering
Fluid Flow and Transfer Processes

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AU - Mizushima, Jiro

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N2 - The nonaxisymmetric linear stability of spherical Couette flow is investigated numerically when the ratio of gap width to inner sphere radius (R2 - R1)/R1 = 0.5. The basic flow becomes unstable at Rec = 1245 and the associated azimuthal wave number is nc = 5, which agrees remarkably well with the experimental results by Egbers and Rath [Acta Mech. 81, 3 (1990)]. The marginal mode is oscillatory and has a distinctive wavy structure around the equator and spirals extended in each hemisphere. Sufficiently large spatial resolution is found to be required in order to avoid serious underestimation of the critical Reynolds number.

AB - The nonaxisymmetric linear stability of spherical Couette flow is investigated numerically when the ratio of gap width to inner sphere radius (R2 - R1)/R1 = 0.5. The basic flow becomes unstable at Rec = 1245 and the associated azimuthal wave number is nc = 5, which agrees remarkably well with the experimental results by Egbers and Rath [Acta Mech. 81, 3 (1990)]. The marginal mode is oscillatory and has a distinctive wavy structure around the equator and spirals extended in each hemisphere. Sufficiently large spatial resolution is found to be required in order to avoid serious underestimation of the critical Reynolds number.

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The nonaxisymmetric instability of the wide-gap spherical Couette flow

Abstract

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