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An experimental study of the instability of the laminar Ekman boundary layer

Published online by Cambridge University Press:  28 March 2006

Alan J. Faller
Alan J. Faller
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, Mass.
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Abstract

This study concerns the stability of the steady laminar boundary-layer flow of a homogeneous fluid which occurs in a rotating system when the relative flow is slow compared to the basic speed of rotation. Such a flow is called an Ekman boundary-layer flow after V. W. Ekman who considered the theory of such flows with application to the wind-induced drift of the surface waters of the ocean.

Ekman flow was produced in a large cylindrical rotating tank by withdrawing water from the centre and introducing it at the rim. This created a steady-state symmetrical vortex in which the flow from the rim to the centre took place entirely in the shallow viscous boundary layer at the bottom. This boundary-layer flow became unstable above the critical Reynolds number $Re_c = vD|v = 125 \pm 5$ where v is the tangential speed of flow, $D = (v| \Omega)^{\frac {1}{2}}$ is the characteristic depth of the boundary layer, v is the kinematic viscosity, and Ω is the basic speed of rotation. The initial instability was similar to that which occurs in the boundary layer on a rotating disk, having a banded form with a characteristic angle to the basic flow and with the band spacing proportional to the depth of the boundary layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 15 , Issue 4 , April 1963 , pp. 560 - 576
Copyright
© 1963 Cambridge University Press

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