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Delayed separation in eastward, rotating flow on a β-plane

Published online by Cambridge University Press:  20 April 2006

M. R. Foster
M. R. Foster
Affiliation:
Department of Aeronautical and Astronautical Engineering, The Ohio State University
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Abstract

We consider the small-Rossby-number flow of a fluid past an obstacle in a coordinate frame in which the rotation rate varies linearly in the direction normal to the flow in a manner that models the variation of the Coriolis force for midlatitude planetary motions. The eastward flow is characterized by strong upstream divergence of the streamlines like that noted by Davies & Boyer (1982), and a similarly severe streamline convergence in the lee of the obstacle. Such a structure occurs for small values of the β-parameter that measures the importance of the lateral angular-velocity variation. In this parameter range, Rossby waves occur, but are confined to a narrow region in the lee of the object. The presence of these waves modifies the edge velocity ‘seen’ by the Stewartson quarter layer in such a way as to delay the onset of separation beyond what one might expect based on the analysis of Walker & Stewartson (1974) for a flow without beta-effect.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 155 , June 1985 , pp. 59 - 75
Copyright
© 1985 Cambridge University Press

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References

Bender, C. M. & Orszag, S. A. 1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill.
Buckmaster, J. 1969 Separation and magnetohydrodynamics. J. Fluid Mech. 38, 481.Google Scholar
Crissali, A. J. & Walker, J. D. A. 1976 Non-linear effects for the Taylor-column problem for a hemisphere. Phys. Fluids 19, 1661.Google Scholar
Davies, P. A. & Boyer, D. L. 1982 Flow past a circular cylinder on a β-plane. Phil. Trans. R. Soc. Lond. A 306, 533.Google Scholar
Foster, M. R. 1972 The flow caused by the differential rotation of a right circular cylindrical depression in one of two rapidly rotating parallel planes. J. Fluid Mech. 53, 647.Google Scholar
Hocking, L. M. 1967 Boundary and shear layers in a curved rotating pipe. J. Math. and Phys. Sci. 1, 123.Google Scholar
Holton, J. R. 1979 An Introduction to Dynamic Meteorology. 2nd edn. Academic.
Leibovich, S. 1967 Magnetohydrodynamic flow at a rear stagnation point. J. Fluid Mech. 19, 401.Google Scholar
McCartney, M. S. 1975 Inertial Taylor columns on a beta plane. J. Fluid Mech. 68, 71.Google Scholar
Merkine, L.-O. 1980 Flow separation on a β-plane. J. Fluid Mech. 99, 399.Google Scholar
Page, M. A. 1982 Flow separation in a rotating annulus with bottom topography. J. Fluid Mech. 66, 303.Google Scholar
Walker, J. D. A. & Stewartson, K. 1972 The flow past a circular cylinder in a rotating frame. Z. angew. Math. Phys. 23, 745.Google Scholar
Walker, J. D. A. & Stewartson, K. 1974 Separation and the Taylor-column problem for a hemisphere. J. Fluid Mech. 66, 767.Google Scholar
White, W. B. 1971 A Rossby wake due to an island in an eastward current. J. Phys. Oceanogr. 1, 161.Google Scholar