E3S Web Conf.
Volume 40, 2018River Flow 2018 - Ninth International Conference on Fluvial Hydraulics
|Number of page(s)||8|
|Section||Fluid mechanics and sediment processes|
|Published online||05 September 2018|
A simple non-equilibrium bedload transport equation for the formation of dune in a shallowwater flow over an erodible bed
Departamento de Ingeniería Mecánica y Minera, University of Jaén, 23071 Jaén, Spain
2 Centro de Estudios Avanzados en Ciencias de la Tierra, University of Jaén, 23071 Jaén, Spain
In this work, we consider the long-standing problem of capturing dune formation in an erodible-bed channel at subcritical speed by using a reduced order model of depth-averaged equations. The pioneering study by Reynolds  showed that the standard Saint-Venant-Exner equations are unconditionally stable at subcritical Froude number. Hence, the use of depthaveraged flow equations, which are commonly used by the hydraulic community, prevents the formation of bedforms as dunes. Recently, Cañada-Pereira & Bohorquez  have proposed a simple sediment transport formulation able to capture the formation of dune when coupled with the Saint-Venant equations. We replace the standard Exner equation with a non-equilibrium sediment transport equation that includes the following necessary ingredients: first, a phase shift in the particle entrainment rate; second, a particle diffusivity and an eddy viscosity. Subsequently, we solve the linear stability problem of an erodiblebed channel and show that the neutral curve properly captures the bed instability both in subcritical regime (i.e. dune) and supercritical flow (i.e. antidune and roll wave). Finally, we corroborate the capabilities of the model by means of non-linear numerical simulations which reproduce the growth of dune and antidune in agreement with experiments.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
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