The University of Southampton
University of Southampton Institutional Repository

Further perspectives on the evolution of bed material waves in alluvial channels

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
0197-9337
115-120
Cao, Z.
c541462a-b279-4c97-910d-69a6726c57c6
Carling, P.A.
8d252dd9-3c88-4803-81cc-c2ec4c6fa687
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), 115-120. (doi:10.1002/esp.1157).

Record type: Article

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.

This record has no associated files available for download.

More information

Published date: 2005
Keywords: sediment transport, alluvial rivers, bed material wave, hyperbolic equationsdispersion, mass conservation law

Identifiers

Local EPrints ID: 58065
URI: http://eprints.soton.ac.uk/id/eprint/58065
ISSN: 0197-9337
PURE UUID: aa30b126-b50d-4866-bc13-382183f0fd07

Catalogue record

Date deposited: 11 Aug 2008
Last modified: 15 Mar 2024 11:09

Export record

Altmetrics

Contributors

Author: Z. Cao
Author: P.A. Carling

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×