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Boundary-layer separation of a two-layer rotating flow on a β-plane

Published online by Cambridge University Press:  21 April 2006

Lee-Or Merkine  and
Leonid Brevdo
Lee-Or Merkine
Affiliation:
Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel
Leonid Brevdo
Affiliation:
Geophysical Fluid Dynamics Laboratory/NOAA, Princeton University, Princeton, NJ 08540, USA
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Abstract

The problem of quasi-geostrophic two-layer flow past a vertical cylinder on a β-plane is investigated analytically and numerically. Two parameter regimes are considered: (i) 0 ≤ E½/ε ≤ ∞ and β = O(1); (ii) E½/ε [Gt ] 1 and βε/E½ = O(1). ε is the Rossby number, E is the Ekman number and β is the beta parameter. In the first parameter regime the nonlinear interior and boundary-layer equations are integrated to determine if and when the wall shear stress vanishes so that an estimate of the condition for separation in the classical sense can be obtained. The results seem to explain the enhancement/suppression of separation in retrograde/prograde flows and the east-west asymmetry observed in the experiments of Boyer & Davies (1982). In the second parameter regime the analysis is linear and the vorticity balance is dominated by the β-effect and Ekman suction. When the flow at infinity is vertically sheared, two large standing interior eddies can be generated next to the cylinder. Only the interior solutions are given in (ii) since the boundary-layer flow is irrelevant to the large-scale behaviour.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 167 , June 1986 , pp. 31 - 48
Copyright
© 1986 Cambridge University Press

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