Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-06T02:06:15.287Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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