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

Wilcox, David C. (1972) The motion of a plate in a rotating fluid at an arbitrary angle of attack. Journal of Fluid Mechanics, 56 (2). pp. 221-240. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20120809-105555197

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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.


Item Type:Article
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http://dx.doi.org/10.1017/S0022112072002824DOIUNSPECIFIED
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=372652&fulltextType=RA&fileId=S0022112072002824PublisherUNSPECIFIED
Additional Information:© 1972 Cambridge University Press. Received September 23 1971. Revised April 3 1972. Published Online March 29 2006. The author is greatly indebted to Professor P. G. Saffman of the California Institute of Technology for his patient assistance and his helpful comments and suggestions during the course of this work.
Record Number:CaltechAUTHORS:20120809-105555197
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120809-105555197
Official Citation: David C. Wilcox (1972). The motion of a plate in a rotating fluid at an arbitrary angle of attack. Journal of Fluid Mechanics, 56 , pp 221-240 doi:10.1017/S0022112072002824
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33048
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:09 Aug 2012 18:10
Last Modified:26 Dec 2012 15:55

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