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The Quarterly Journal of Mechanics and Applied Mathematics 1990 43(1):87-106; doi:10.1093/qjmam/43.1.87
© 1990 by Oxford University Press
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FREE-SURFACE FLOW OF A STREAM OBSTRUCTED BY AN ARBITRARY BED TOPOGRAPHY

A. C. KING1,{dagger} and M. I. G. BLOOR2

( 1Department of Theoretical Mechanics, University of Nottingham Nottingham NG7 2RD
2Department of Applied Mathematical Studies, University of Leeds Leeds LS2 9JT )

{dagger} Permanent address: Department of Mathematics, University of Keele, Keele, Staffordshire ST5 5BG.

The steady, two-dimensional, free-surface flow of a stream which is obstructed by an arbitrarily-curved-bed topography is considered. A conformal-mapping method is used to reformulate the fluid-mechanics problem as a pair of coupled nonlinear integral and integrodifferential equations. Linearized and numerical nonlinear solutions to these equations are found for a variety of topographies.


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