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Weir flows and waterfalls

Published online by Cambridge University Press:  26 April 2006

Frédéric Dias  and
E. O. Tuck
Frédéric Dias
Affiliation:
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, USA Present address: Université de Nice, INLN, UMR CNRS 129, Parc Valrose, 06034 Nice cedex, France.
E. O. Tuck
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, S.A. 5001, Australia
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Abstract

Two-dimensional free-surface flows, which are uniform far upstream in a channel of finite depth that ends suddenly, are computed numerically. The ending is in the form of a vertical wall, which may force the flow upward before it falls down forever as a jet under the effect of gravity. Both subcritical and supercritical solutions are presented. The subcritical solutions are a one-parameter family of solutions, the single parameter being the ratio between the height of the wall and the height of the uniform flow far upstream. On the other hand, the supercritical solutions are a two-parameter family of solutions, the second parameter being the Froude number. Moreover, for some combinations of the parameters, it is shown that the solution is not unique.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 230 , September 1991 , pp. 525 - 539
Copyright
© 1991 Cambridge University Press

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