Exact Discontinuous Solutions of Exner’s Bed Evolution Model: Simple Theory for Sediment Bores |
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Authors: | Ethan J Kubatko Joannes J Westerink |
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Affiliation: | 1Postdoctoral Fellow, Institute for Computational Engineering and Sciences, Univ. of Texas at Austin, Austin, TX 78712; formerly, Postdoctoral Researcher, Dept. of Civil Engineering and Geological Sciences, Univ. of Notre Dame, 156 Fitzpatrick Hall, Notre Dame, IN 46556 (corresponding author). E-mail: ekubatko@ices.utexas.edu 2Professor, Dept. of Civil Engineering and Geological Sciences, Univ. of Notre Dame, 156 Fitzpatrick Hall, Notre Dame, IN 46556. E-mail: jjw@photius.ee.nd.edu
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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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Keywords: | Sediment River beds Hydraulic models Erosion Fluid flow |
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