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The flow induced by the transverse motion of a thin disk in its own plane through a contained rapidly rotating viscous liquid

  • D. W. Moore (a1), P. G. Saffman (a2) and T. Maxworthy (a3)
Abstract

A thin circular disk translates slowly in its own plane transverse to the axis of rotation of parallel plane boundaries filled with viscous incompressible liquid. It is shown that the indeterminateness of the geostrophic flow is removed by constraints imposed by the dynamics of free shear layers (Stewartson layers), which surround a Taylor column whose boundary is not a stream surface. Fluid particles cross the Taylor column at the expense of deflexion through a finite angle. A comparison is made with the flow past a fat body (Jacobs 1964), where the geostrophie flow is determined without appeal to the dynamics of the shear layers. The problem is also considered for a disk in an unbounded fluid, and it is shown that to leading order there is no disturbance.

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References
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Jacobs, S.1964 The Taylor column problem. J. Fluid Mech. 20, 581.
Jahnke, E. & Emde, F.1945 Tables of Functions. New York: Dover.
Moore, D. W. & Saffman, P. G.1969 The structure of free vertical shear layers in a rotating fluid and the motion produced by a slowly rising body. Phil. Trans. Roy. Soc. Land. A 264, 597.
Stewartson, K.1953 On the slow motion of an ellipsoid in a rotating fluid Quart. J. Mech. appl. Math. 6, 141.
Stewartson, K.1966 On almost rigid rotations. Part 2 J. Fluid Mech. 26, 131.
Stewartson, K.1967 On slow transverse motion of a sphere through a rotating fluid J. Fluid Mech. 30, 357.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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