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IMA Journal of Applied Mathematics Advance Access published online on October 24, 2007
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxm049
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Influence of rapid changes in a channel bottom on free-surface flows

B. J. Binder

School of Mathematical Sciences, University of Adelaide, Adelaide 5005, Australia

F. Dias

Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan, UniverSud, 61 Avenue President Wilson, F-94230 Cachan, France

J.-M. Vanden-Broeck{dagger}

School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK

{dagger} Email: j.vanden-broeck{at}uea.ac.uk. Present address: Department of Mathematics, University College London, Gover Street, London WC1E 6BT, UK

Received on January 26, 2007; Accepted on June 1, 2007

Two-dimensional non-linear free-surface flows in a channel bounded below by an uneven bottom with rapid changes are considered. Numerical solutions are computed by a boundary integral equation method similar to that first introduced by King & Bloor (1987, J. Fluid Mech., 182, 193–208). Free-surface flows past localized disturbances, steps and sluice gates are calculated. In addition, weakly non-linear solutions are discussed.

Keywords: free-surface flow; boundary integral equation method; potential flow.


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