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Sink flow in a rotating basin

Published online by Cambridge University Press:  19 April 2006

C. Kranenburg
Affiliation:
Department of Civil Engineering, Delft University of Technology, The Netherlands

Abstract

The flow of a homogeneous viscous liquid towards a sink in the interior of a rotating basin with a free surface, a horizontal bottom and a vertical side wall is considered. The conditions assumed are such that an Ekman layer occurs at the bottom beyond a small distance from the sink. A first-order correction to the Ekman model accounting for the influence of the inertial terms in the equations of motion is given for a special case. It is shown theoretically and experimentally that eccentric withdrawal from a circular basin causes a vortex at the sink and a counter-rotating gyre attached to the far wall.

Type
Research Article
Copyright
© 1979 Cambridge University Press

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References

Barcilon, V. 1967 On the motion due to sources and sinks distributed along the vertical boundary of a rotating fluid. J. Fluid Mech. 27, 551560.Google Scholar
Brown, S. N. & Stewartson, K. 1976 Asymptotic methods in the theory of rotating fluids, in Asymptotic Methods and Singular Perturbations. Proc. Symp. Appl. Math. AMS & SIAM.
Burggraf, O. R., Stewartson, K. & Belcher, R. J. 1971 Boundary layer induced by a potential vortex. Phys. Fluids 14, 18211833.Google Scholar
Burggraf, O. R. & Foster, M. R. 1977 Continuation or breakdown in tornado-like vortices. J. Fluid Mech. 80, 685703.Google Scholar
Goossens, L. H. J. & Van Pagee, J. A. 1977 Modelling of the near field due to air injection in big reservoirs. Proc. 17th Cong. IAHR 1, 551560.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Hide, R. 1968 On source—sink flows in a rotating fluid. J. Fluid Mech. 32, 737764.Google Scholar
Kranenburg, C. 1978 On the destratification of lakes and reservoirs using bubble columns. Delft Univ. Tech. The Netherlands, Rep. no. 78–1.Google Scholar
Kuo, H.-H. & Veronis, G. 1971 The source—sink flow in a rotating system and its oceanic analogy. J. Fluid Mech. 45, 441464.Google Scholar
Lewellen, W. S. 1962 A solution for three-dimensional vortex flows with strong circulation. J. Fluid Mech. 14, 420432.Google Scholar
Nayfeh, A. H. 1973 Perturbation Methods. John Wiley.
Turner, J. S. 1966 The constraints imposed on tornado-like vortices by the top and bottom boundary conditions. J. Fluid Mech. 25, 377400.Google Scholar