Abstract
In this paper, the disturbances to a uniformly rotating ideal fluid with a sphere moving steadily along the axis of rotation are analysed by using linearization theory, the equations of disturbance, pressure and disturbance stream function governing the stability of motion are derived based on the assumption that the flow is rotational symmetric. The equation of disturbance stream function is analysed with the method of normal modes, and the constraints on wave number and wave velocity of the nontrivial neutral disturbances are established and the exact expression of the neutral disturbances are obtained. The conclusion is drawn that three are three kinds of possible forms of neutral disturbances.
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References
J. Proudman, On the motion of solids in a liquid possessing vorticity,Proc. Roy. Soc. A,92 (1916), 408–424.
G. I. Taylor, Motion of solids in fluids when the flow is not irrotational.,Proc. Roy. Soc. A,93 (1917), 99–113.
S. Goldstein (editor),Modern Developments in Fluid Dynamics, Vol. I. Oxford University Press (1938), 47.
H. Honji and T. Hosoyamada, Instability of the rotating gravity flow down a slope,Reports of Research Institute for Applied Mechanics,35, 105 (1989), 55–64.
V. A. Gorodtsov, Behavior of a sphere in an ideal uniformly stratified medium,Fluid Mech. Res.,21, 6 (1992), 100–106.
T. K. V. Iyengar and D. S. Charya, Slow steady rotation of an approximate sphere in an incompressible micropolar fluid,Int. J. Eng. Sci.,33, 6 (1995), 867–877.
G. I. Taylor, The motion of a sphere in a rotating liquid,Proc. Roy. Soc. A,102 (1922), 180–189.
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Communicated by Dai Shiqing
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Jiachun, L. Disturbances to a rotating fluid with a sphere moving along the axis of rotation. Appl Math Mech 19, 861–867 (1998). https://doi.org/10.1007/BF02458241
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DOI: https://doi.org/10.1007/BF02458241