Abstract
We study flow stability in a thin spherical layer with respect to small disturbances. It is shown that for each given layer thickness there is a sequence of critical Reynolds numbers above which the motion is unstable. In its form, the critical disturbance is reminiscent of the secondary flow which develops upon loss of stability of the basic fluid flow between rotating cylinders (Taylor problem).
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Yu. G. Ovseenko, “Motion of a viscous fluid between two rotating spheres,” Izv. vuzov, Matematika no. 4, 1963.
L. D. Landau and E. M. Lifshits, Mechanics of Continua [in Russian], Gostekhizdat, Moscow, 1953.
Yu. K. Bratukhin, “Estimate of the critical Reynolds number for fluid flow between two rotating spherical surfaces,” PMM, vol. 25, no. 5, 1961.
V. S. Sorokin, “Nonlinear phenomena in closed cavities near the critical Reynolds numbers,” PMM, vol. 25, no. 2, 1961.
V. I. Yakushin, “Spectrum of small disturbances of fluid flow between rotating spherical surfaces,” PMM, vol. 31, no. 3, 1967.
V. V. Voevodin, “Some methods of solution of the complete eigenvalue problem,” Zh. vychislit. matem. i matem. fiz., vol. 2, no. 1, 1962.
G. N. Khlebutin, “Stability of fluid motion between rotating and stationary concentric spheres,” Izv. AN SSSR, MZhG [Fluid Dynamics], vol. 3, no. 6, 1968.
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The author wishes to thank M. I. Shliomis for his continued interest in this study.
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Yakushin, V.I. Instability of fluid motion in a thin spherical layer. Fluid Dyn 4, 83–85 (1969). https://doi.org/10.1007/BF01032401
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DOI: https://doi.org/10.1007/BF01032401