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Boundary-layer separation of rotating flows past surface-mounted obstacles

Published online by Cambridge University Press:  26 April 2006

K. J. Richards ,
D. A. Smeed ,
E. J. Hopfinger  and
G. Chabert D'Hières
K. J. Richards
Affiliation:
Department of Oceanography, The University, Southampton SO9 5NH, UK Present address: James Rennell Centre for Ocean Circulation, Gamma House, Chilworth Research Centre, Southampton SO1 7NS, UK.
D. A. Smeed
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Cambridge University, Silver St, Cambridge, CB3 9EW, UK
E. J. Hopfinger
Affiliation:
Institut de Mécanique de Grenoble, Domaine Universitaire, BP 53X, 38041 Grenoble Cedex, France
G. Chabert D'Hières
Affiliation:
Institut de Mécanique de Grenoble, Domaine Universitaire, BP 53X, 38041 Grenoble Cedex, France
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Abstract

This paper describes laboratory experiments on the flow over a three-dimensional hill in a rotating fluid. The experiments were carried out in towing tanks, placed on rotating tables. Rotation is found to have a strong influence on the separation behind the hill. The topology of the separation is found to be the same for all the flows examined. The Rossby number R in the experiments is of order 1, the maximum value being 6. The separated flow is dominated by a single trailing vortex. In the majority of cases the surface stress field has a single separation line and there are no singular points. In a few experiments at the highest Rossby numbers the observations suggest more complex stress fields but the results are inconclusive.

A criterion for flow separation is sought. For values of D/L > 1, where D is the depth of the flow and L the lengthscale of the hill, separation is found to be primarily dependent on R. At sufficiently small values of R separation is suppressed and the flow remains fully attached.

Linear theory is found to give a good estimate for the critical value of R for flow separation. For hills with a moderate slope (slope ≤ 1) this critical value is around 1, decreasing with increasing slope. It is postulated that the existence of a single dominant trailing vortex is due to the uplifting and subsequent turning of transverse vorticity generated by surface pressure forces upstream of the separation line.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 237 , April 1992 , pp. 343 - 371
Copyright
© 1992 Cambridge University Press

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