Further perspectives on the evolution of bed material waves in alluvial channels
Further perspectives on the evolution of bed material waves in alluvial channels
In one-dimensional mathematical models of fluvial flow, sediment transport and morphological evolution, the governing equations based on mass and momentum conservation laws constitute a hyperbolic system. Succinctly, the hyperbolic nature excludes dispersion or diffusion operators, which is well known in the context of differential equations. There is no doubt that the so-called ‘dispersion’ argument for bed material wave evolution is questionable, as we have explicitly asserted. Surprisingly, in a recent communication, the authors of the ‘dispersion’ argument suggest that dispersion is not precluded in hyperbolic systems. We provide herein further perspectives to help explain that the dispersion argument is neither appropriate nor necessary for interpreting bed material wave evolution. Also the continuity equations involved are addressed to prompt wider understanding of their significance. In particular, the continuity equation of the water–sediment mixture proposed by the authors of the ‘dispersion’ argument is proved to be incorrect, and inevitably their reasoning based on it is problematic.
sediment transport, alluvial rivers, bed material wave, hyperbolic equationsdispersion, mass conservation law
115-120
Cao, Z.
c541462a-b279-4c97-910d-69a6726c57c6
Carling, P.A.
8d252dd9-3c88-4803-81cc-c2ec4c6fa687
2005
Cao, Z.
c541462a-b279-4c97-910d-69a6726c57c6
Carling, P.A.
8d252dd9-3c88-4803-81cc-c2ec4c6fa687
Cao, Z. and Carling, P.A.
(2005)
Further perspectives on the evolution of bed material waves in alluvial channels.
Earth Surface Processes and Landforms, 30 (1), .
(doi:10.1002/esp.1157).
Abstract
In one-dimensional mathematical models of fluvial flow, sediment transport and morphological evolution, the governing equations based on mass and momentum conservation laws constitute a hyperbolic system. Succinctly, the hyperbolic nature excludes dispersion or diffusion operators, which is well known in the context of differential equations. There is no doubt that the so-called ‘dispersion’ argument for bed material wave evolution is questionable, as we have explicitly asserted. Surprisingly, in a recent communication, the authors of the ‘dispersion’ argument suggest that dispersion is not precluded in hyperbolic systems. We provide herein further perspectives to help explain that the dispersion argument is neither appropriate nor necessary for interpreting bed material wave evolution. Also the continuity equations involved are addressed to prompt wider understanding of their significance. In particular, the continuity equation of the water–sediment mixture proposed by the authors of the ‘dispersion’ argument is proved to be incorrect, and inevitably their reasoning based on it is problematic.
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Published date: 2005
Keywords:
sediment transport, alluvial rivers, bed material wave, hyperbolic equationsdispersion, mass conservation law
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Local EPrints ID: 58065
URI: http://eprints.soton.ac.uk/id/eprint/58065
ISSN: 0197-9337
PURE UUID: aa30b126-b50d-4866-bc13-382183f0fd07
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Date deposited: 11 Aug 2008
Last modified: 15 Mar 2024 11:09
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Author:
Z. Cao
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