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Rotating flow over shallow topographies

Published online by Cambridge University Press:  29 March 2006

Arsalan Vaziri  and
Don L. Boyer
Arsalan Vaziri
Affiliation:
Department of Civil Engineering, University of Delaware, Newark, Delaware
Don L. Boyer
Affiliation:
Department of Civil Engineering, University of Delaware, Newark, Delaware Present address: National Science Foundation, Washington, D.C.
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Abstract

The flow of a rotating homogeneous incompressible fluid over various shallow topographies is investigated. In the physical system considered, the rotation axis is vertical while the topography and its mirror image are located on the lower and upper of two horizontal plane surfaces. Upstream of the topographies and outside the Ekman layers on the bounding planes the fluid is in a uniform free-stream motion. An analysis is considered in which E [Lt ] 1, Ro ∼ E½, H/D ∼ E0, and h/D ∼ E½, where E is the Ekman number, Ro the Rossby number, H/D the fluid depth to topography width ratio and h/D the topography height-to-width ratio. The governing equation for the lowest-order interior motion is obtained by matching an interior geostrophic region with Ekman boundary layers along the confining surfaces. The equation includes contributions from the non-linear inertial, Ekman suction, and topographic effects. An analytical solution for a cosine-squared topography is given for the case in which the inertial terms are negligible; i.e. Ro [Lt ] E½. Numerical solutions for the non-linear equations are generated for both cosine-squared and conical topographies. Laboratory experiments are presented which are in good agreement with the theory advanced.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 1 , 15 November 1971 , pp. 79 - 95
Copyright
© 1971 Cambridge University Press

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