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Two-layer rotating steady viscous flow over long ridges

Published online by Cambridge University Press:  20 April 2006

Don L. Boyer
Don L. Boyer
Affiliation:
Department of Mechanical Engineering, University of Wyoming, Laramie
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Abstract

The flow of a rotating, two-layer fluid system over long ridges of constant cross-section is considered. Homogeneous incompressible fluids of constant, but different, density are confined between two ‘infinite’ horizontal plane surfaces which rotate at a constant angular velocity about a vertical axis. The ridge is located on the lower surface while upstream of the ridge each fluid is in uniform motion in a direction normal to the ridge. Solutions are obtained for both an f-plane and a β-plane under the following restrictions: E [Lt ] 1, Ro ∼ E½, S ∼ O(1), H/L ∼ O(1), d/L ∼ O(1) and h/L ∼ E½ where E is the Ekman number, Ro is the Rossby number, S is a stratification parameter, H/L is the two-fluid depth to ridge width ratio, d/L is the lower fluid depth to ridge width ratio and h/L is the aspect ratio of the ridge. This set of restrictions assures that viscosity is important in considering the dynamics of the system. Furthermore the restrictions are ones that make laboratory experimentation feasible. Solutions are also presented for the non-viscous case (i.e. E = O), and are compared with their viscous counterparts. The importance of viscosity in this physical system is thus demonstrated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 111 , October 1981 , pp. 1 - 14
Copyright
© 1981 Cambridge University Press

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