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Free-surface flow over a step

Published online by Cambridge University Press:  21 April 2006

A. C. King  and
M. I. G. Bloor
A. C. King
Affiliation:
Department of Mathematics and Statistics, City of Birmingham Polytechnic, Birmingham B42 2TH, UK Present address: Department of Theoretical Mechanics, University of Nottingham, University Park, NG7 2RD, UK.
M. I. G. Bloor
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds LS2 9JT, UK
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Abstract

A transformation technique is used to solve the problem of steady free-surface flow of an ideal fluid over a semi-infinite step in the bottom. Application of the exact free-surface condition results in a nonlinear integro-differential equation for the free-surface angle and solutions of this equation are dependent on step height and Froude number. Linearized solutions, based upon small step height are presented and indicate that the nature of the free surface formed depends on whether the upstream flow is subcritical or supercritical. As the step height is increased, solutions to the exact nonlinear equations are obtained using the predictions of the linear theory, or possibly a previous nonlinear solution, as an initial estimate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 182 , September 1987 , pp. 193 - 208
Copyright
© 1987 Cambridge University Press

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