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Transverse dam-break waves

Published online by Cambridge University Press:  07 October 2014

S. Karimpour Ghannadi  and
Vincent H. Chu
S. Karimpour Ghannadi
Affiliation:
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, QC, H3A 0C3, Canada
Vincent H. Chu*
Affiliation:
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, QC, H3A 0C3, Canada
*
†Email address for correspondence: vincent.chu@mcgill.ca
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Abstract

Numerical simulations of the transverse dam-break waves (TDWs) produced by the sudden removal of a gate on the side of a waterway are conducted based on the shallow-water equations to find solutions to a family of water-diversion problems. The Froude numbers in the main flow identify the members of the family. The depth and discharge profiles are analysed in terms of Ritter’s similarity variable. For subcritical main flow, the waves are comprised of a supercritical flow expansion followed by a subcritical outflow. For supercritical main flow, on the other hand, the waves are analogous to the Prandtl–Meyer expansion in gas dynamics. The diversion flow rate of two-dimensional TDWs on a flat bed is 55 % greater than the one-dimensional flow rate of Ritter in the limiting case of zero main flow, and approaches the rate of Ritter in the other limit when the value of the Froude number in the main flow approaches infinity. The diversion flow rate over a weir is generally higher than the rate over a flat bed depending on the Froude number of the main flow. These numerical simulation results are consistent with laboratory observations.

JFM classification

Mathematical Foundations: Computational methods Geophysical and Geological Flows: Geophysical and Geological Flows Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 758 , 10 November 2014 , R2
Copyright
© 2014 Cambridge University Press 

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