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The eddy structure in Stokes flow in a cavity

Published online by Cambridge University Press:  26 April 2006

P. N. Shankar
P. N. Shankar
Affiliation:
Computational and Theoretical Fluid Dynamics Division, National Aeronautical Laboratory, Bangalore 560017, India
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Abstract

Stokes flow in a two-dimensional cavity of rectangular section, induced by the motion of one of the walls, is considered. A direct, efficient calculational procedure, based on an eigenfunction expansion, is used to study the eddy structure in the cavity. It is shown that some of the results of earlier studies are quantitatively in error. More importantly, two interesting questions, namely the extent of the symmetry of the corner eddies and their relationship to the large-eddy structure are settled. By carefully examining the rather sudden change in the main eddy structure for cavities of depth around 1.629, it is shown that the main eddies are formed by the merger of the primary corner eddies; the secondary corner eddies then become the primary corner eddies and so on. Thus, in the evolution of the large-eddy structure the corner eddies, in some sense, play the role of progenitors. This explicit prediction should be experimentally verifiable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 250 , May 1993 , pp. 371 - 383
Copyright
© 1993 Cambridge University Press

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