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The motion generated by a body moving along the axis of a uniformly rotating fluid

Published online by Cambridge University Press:  29 March 2006

W. G. Pritchard
W. G. Pritchard
Affiliation:
Department of Mathematics, The University of Manchester Institute of Science and Technology
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Abstract

Experiments have been made to investigate the motion generated by a body moving along the axis of a uniformly rotating fluid.

Part of the investigation concerns the motion generated in a cylinder whose radial dimensions are much greater than those of the body. Measurements have been made of the velocities of particles on the axis of rotation both ahead of and behind the body, and the results indicate that there is a significant axial motion generated by the body over a wide range of Rossby numbers. A measurement of the instantaneous velocity profile ahead of the body, determined as a function of the radius, agrees fairly well with a low Rossby number calculation of the flow due to a circular disk (Morgan 1951). In addition, the forward influence of the body has been measured as a function of the Rossby number and from these results it is suggested that the body has a finite influence far upstream at all Rossby numbers and that the blocking phenomenon first reported by Taylor (1922) probably occurs for all values of the Rossby number (UΩa) less than a critical value which is about 0·7.

Experiments have also been made in a long cylindrical tube which acts as a wave guide. At large distances from the body the separate effects of the various modes can be observed and hence it is possible to measure the flow corresponding to an individual wave-number: these measurements show that, as a result of the Doppler effect, the motion a large distance ahead of the body is different from that far behind (see Lighthill 1967). Moreover, the experiments indicate that no disturbances propagate ahead of the body when its velocity exceeds the maximum group velocity in the fluid, but that disturbances trail behind the body when its velocity is far in excess of the maximum group velocity. Measurements of the maximum group velocity are in good agreement with the theoretical value.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 39 , Issue 3 , 27 November 1969 , pp. 443 - 464
Copyright
© 1969 Cambridge University Press

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