Modeling the Spatial Evolution of Roll Waves with Diffusive Saint Venant Equations
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Volume 141, Issue 2
Abstract
In this paper, modeling the spatial evolution of roll waves with diffusive Saint Venant equations is examined. A momentum diffusion term is added to the equations to describe turbulent normal stress occurring in extremely nonuniform roll waves. Roll-wave flows with the same hydraulic conditions as in Brock’s experiment are simulated so as to obtain time-averaged wave crest and trough depths. The magnitude of the diffusion effect is found to have significant influence on the spatial growth rate of the wave amplitude. Simulated wave crest and trough depths along the channel agree with experimental data only when the proper turbulent viscosity value is selected. This study indicates that the nondiffusive Saint Venant equations are unable to describe roll-wave flows because the wave amplitude is largely overestimated. The Saint Venant–type model should incorporate comprehensive turbulent stresses and appropriate closure approaches for predicting the spatial evolution of roll waves.
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Acknowledgments
The research presented in this paper is supported by the USC Foundation for Cross-Connection Control and Hydraulic Research.
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Journal of Hydraulic Engineering
Volume 141 • Issue 2 • February 2015
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© 2014 American Society of Civil Engineers.
History
Received: Mar 7, 2014
Accepted: Oct 2, 2014
Published online: Nov 10, 2014
Published in print: Feb 1, 2015
Discussion open until: Apr 10, 2015
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