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Coupled Batchelor flows in a confined cavity

Published online by Cambridge University Press:  26 April 2006

M. Vynnycky  and
K. Kanev
M. Vynnycky
Affiliation:
Tohoku National Industrial Research Institute, 4-2-1 Nigatake, Miyagino-Ku, Sendai, 983 Japan
K. Kanev
Affiliation:
Tohoku National Industrial Research Institute, 4-2-1 Nigatake, Miyagino-Ku, Sendai, 983 Japan Present address: Visual Science Laboratory, Inc., Awajicho MH bldg. 2–21 Kanda Awajicho, Chiyoda-Ku, Tokyo, 101 Japan
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Abstract

Steady, inviscid, incompressible two-dimensional flow in a quarter-circular cavity containing two vortex patches is investigated. A two-parameter family of solutions, characterized by any two out of the positions of the separation and reattachment points of the main eddy, the tangential velocity at separation and the ratio of the core vorticities, is identified and computed numerically. It is found that solutions can only be obtained for a rather narrow band of combinations of these parameters; the reasons for this constraint are discussed. Finally, we consider whether any of the coupled Batchelor flow solutions actually does represent the limit of high Reynolds number flow by comparing the inviscid results with those of earlier Navier–Stokes computations (Vynnycky & Kimura 1994). Agreement for the position of the dividing streamline and the location of the centre of the main core proves to be very encouraging, and suggestions are made as to the possible future development of such a two-eddy model.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 319 , 25 July 1996 , pp. 305 - 322
Copyright
© 1996 Cambridge University Press

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