Exact Discontinuous Solutions of Exner’s Bed Evolution Model: Simple Theory for Sediment Bores
Publication: Journal of Hydraulic Engineering
Volume 133, Issue 3
Abstract
Determining the evolution of the bed of a river or channel due to the transport of sediment was first examined in a theoretical context by Exner in 1925. In his work, Exner presents a simplified bed evolution model derived from the conservation of fluid mass and an “erosion” equation that is commonly referred to as the sediment continuity or Exner equation. Given that Exner’s model takes the form of a nonlinear hyperbolic equation, one expects, depending on the given initial condition of the bed, the formation of discontinuities in the solution in finite time. The analytical solution provided by Exner for his model is the so-called classical or genuine solution of the initial-value problem, which is valid while the solution is continuous. In this paper, using the general theory of nonlinear hyperbolic equations, we consider generalized solutions of Exner’s classic bed evolution model thereby developing a simple theory for the formation and propagation of discontinuities in the bed or so-called sediment bores.
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Acknowledgments
This work was supported by the Morphos-3D Long Wave Hydrodynamics Modeling Work Unit funded through Woolpert Inc. by the U.S. Army Corps of Engineers, Mobile District, under Contract W91278-05-D-0018/003.
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© 2007 ASCE.
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Received: Sep 29, 2005
Accepted: Jun 15, 2006
Published online: Mar 1, 2007
Published in print: Mar 2007
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