Computing Nonhydrostatic Shallow-Water Flow over Steep Terrain
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Volume 134, Issue 11
Abstract
Flood and dambreak hazards are not limited to moderate terrain, yet most shallow-water models assume that flow occurs over gentle slopes. Shallow-water flow over rugged or steep terrain often generates significant nonhydrostatic pressures, violating the assumption of hydrostatic pressure made in most shallow-water codes. In this paper, we adapt a previously published nonhydrostatic granular flow model to simulate shallow-water flow, and we solve conservation equations using a finite volume approach and an Harten, Lax, Van Leer, and Einfeldt approximate Riemann solver that is modified for a sloping bed and transient wetting and drying conditions. To simulate bed friction, we use the law of the wall. We test the model by comparison with an analytical solution and with results of experiments in flumes that have steep (31°) or shallow (0.3°) slopes. The law of the wall provides an accurate prediction of the effect of bed roughness on mean flow velocity over two orders of magnitude of bed roughness. Our nonhydrostatic, law-of-the-wall flow simulation accurately reproduces flume measurements of front propagation speed, flow depth, and bed-shear stress for conditions of large bed roughness.
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Acknowledgments
Testing and validation of our code would not have been possible without data from the U.S. Geological Survey Debris-Flow flume and the dedication and ingenuity of Richard M. Iverson, Matt Logan, and Rick LaHusen of the USGS and many others involved with flume experiments. Support for this research was provided by the U.S. Geological Survey and the Science and Technology Research Program of the U.S. Bureau of Reclamation. Thorough reviews by the Associate Editor and two anonymous reviewers greatly improved the manuscript.
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Published In
Journal of Hydraulic Engineering
Volume 134 • Issue 11 • November 2008
Pages: 1590 - 1602
Copyright
© 2008 ASCE.
History
Received: Aug 9, 2007
Accepted: Apr 22, 2008
Published online: Nov 1, 2008
Published in print: Nov 2008
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