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On the internal shear layers spawned by the critical regions in oscillatory Ekman boundary layers

Published online by Cambridge University Press:  26 April 2006

R. R. Kerswell
R. R. Kerswell
Affiliation:
Department of Mathematics and Statistics, University of Newcastle upon Tyne, Newcastle NE1 7RU, UK
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Abstract

The Ekman boundary layer scalings associated with small oscillatory flows in a rapidly rotating system are well known to break down at the critical latitudes. The effect of these anomalous boundary regions on the interior flow has long been an issue of some concern. We argue, using analytical results derived in a model problem based on Stewartson's (1957) split-disk configuration, that these boundary regions spawn internal shear layers. These shear layers have their natural length scale of E1/3 and carry velocities only O(E1/6) smaller than the Rossby number – where E is the Ekman number – if the boundary is concave away from the fluid at the critical latitude. Otherwise, only a weaker shear layer is produced of length scale E1/5 containing velocities of O(E3/10) smaller than the Rossby number rather than the usual O(E1/5) value for viscous flows in the interior. We show how these layers can carry angular momentum by themselves or more significantly in combination with the interior inviscid flow, so as to influence the mean flow at leading order. These conclusions are then discussed in the context of a precessing oblate spheroid of fluid for which detailed experimental observations are available.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 298 , 10 September 1995 , pp. 311 - 325
Copyright
© 1995 Cambridge University Press

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