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The motion of a plate in a rotating fluid at an arbitrary angle of attack

  • David C. Wilcox (a1)
Abstract

Slow motion of a thin plate at a finite angle of attack in a rotating container filled with a viscous incompressible fluid is analysed. The Rossby and Ekman numbers are assumed to be small. The solution method is developed by studying horizontal translation of an elliptical plate. The plate is shown to carry a stagnant Taylor column with it as it moves. Detailed analysis of the structure of the vertical shear column bounding the Taylor column is circumvented by integrating the equations of motion across the shear column. A jump condition based upon mass conservation in the shear column which relates the geostrophic regions inside and outside the Taylor column results. This jump condition and its method of derivation can be used to analyse arbitrary (slow) motion of any thin plate at any angle of attack.

The fluid motion resulting when a disk moves using all six degrees of freedom at an infinitesimal angle of attack is discussed. The forces and moments on the disk are calculated and the streamlines of the geostrophic flow are displayed.

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References
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Greenspan, H. P.1968 The Theory of Rotating Fluids. Cambridge University Press.
Jacobs, S.1964 The Taylor column problem. J. Fluid Mech. 20, 581.
Moore, D. W. & Saffman, P. G.1969a The structure of free vertical shear layers in a rotating fluid and the motion produced by a slowly rising body. Phil. Trans. Roy. Soc. A 264, 597.
Moore, D. W. & Saffman, P. G.1969b The flow induced by the transverse motion of a thin disk in its own plane through a contained rapidly rotating viscous liquid. J. Fluid Mech. 39, 831.
Pedlosky, J. & Greenspan, H. P.1967 A simple laboratory model for the oceanic circulation. J. Fluid Mech. 27, 291.
Stewartson, K.1966 On almost rigid rotations. Part 2. J. Fluid Mech. 26, 131.
Taylor, G. I.1922 The motion of a sphere in a rotating liquid. Proc. Roy. Soc. A 102, 180.
Wilcox, D. C.1970 The motion of a disk at angle of attack in a rapidly rotating fluid. Ph.D. thesis, California Institute of Technology.
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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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