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AGU: Water Resources Research

 

Keywords

  • Shallow-water equation
  • dam break
  • flood wave
  • analytical solution
  • hodograph transformation
  • Riemann method

Index Terms

  • Mathematical Geophysics: General or miscellaneous
  • Hydrology: Modeling
  • Hydrology: Numerical approximations and analysis
  • Hydrology: Dams

Abstract

WATER RESOURCES RESEARCH, VOL. 44, W01430, 10 PP., 2008
doi:10.1029/2007WR006353

An exact solution for ideal dam-break floods on steep slopes

C. Ancey

School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

R. M. Iverson

U.S. Geological Survey, Cascades Volcano Observatory, Vancouver, Washington, USA

M. Rentschler

School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

R. P. Denlinger

U.S. Geological Survey, Cascades Volcano Observatory, Vancouver, Washington, USA

The shallow-water equations are used to model the flow resulting from the sudden release of a finite volume of frictionless, incompressible fluid down a uniform slope of arbitrary inclination. The hodograph transformation and Riemann's method make it possible to transform the governing equations into a linear system and then deduce an exact analytical solution expressed in terms of readily evaluated integrals. Although the solution treats an idealized case never strictly realized in nature, it is uniquely well-suited for testing the robustness and accuracy of numerical models used to model shallow-water flows on steep slopes.

Received 17 July 2007; accepted 17 October 2007; published 25 January 2008.

Citation: Ancey, C., R. M. Iverson, M. Rentschler, and R. P. Denlinger (2008), An exact solution for ideal dam-break floods on steep slopes, Water Resour. Res., 44, W01430, doi:10.1029/2007WR006353.

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