Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-21T15:15:00.697Z Has data issue: false hasContentIssue false
  • English
  • Français

The Taylor column problem

Published online by Cambridge University Press:  28 March 2006

S.J. Jacobs
S.J. Jacobs
Affiliation:
Pierce Hall, Harvard University
Present address: Department of Meteorology and Oceanography, University of Michigan.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider here flow past an obstacle on the lower of two rotating horizontal planes which bound a viscous fluid. It is found that when the Taylor number is large viscous effects are confined to Ekman boundary layers on the solid surfaces and to a free shear layer coincident with the vertical cylinder circumscribing the bottom obstacle. The flow in the main body of the fluid outside the cylinder proves to be two-dimensional with zero relative vorticity, while inside the cylinder the fluid is stagnant in the rotating frame. The shear layer provides a continuous transition between the exterior and interior of the cylinder, and in addition provides a means by which fluid from the Ekman layers on the horizontal planes is exchanged with fluid outside the Ekman layers and exterior to the circumscribing cylinder. The predicted flow proves to be in agreement with many of the experimental results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 20 , Issue 4 , December 1964 , pp. 581 - 591
Copyright
© 1964 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Greenspan, H. & Howard, L. 1963 On a time-dependent motion of a rotating fluid. J. Fluid Mech. 17, 385–404.Google Scholar
Hide, R. 1961 Origin of Jupiter's great red spot. Nature, Lond., 190, 895–896.Google Scholar
Ibbetson, A. 1963 Private communication.
Stewartson, K. 1953 On the slow motion of an ellipsoid in a rotating fluid. Quart. J. Mech. Appl. Math., 6, 141–162.Google Scholar
Taylor, G. I. 1923 Experiments on the motion of solid bodies in rotating fluids. Proc. Roy. Soc. A, 104, 213–218.Google Scholar