Abstract
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 [1] 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 [2] 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.
Highlights
The prediction of the occurrence of bedforms and its morphology has been a case of study of great interest due to its influence in major engineering problems such as floods and the effects on the landscape in general
Alternative morphodynamic models for dune formation based on the Saint-Venant equations are scarce and require an ad-hoc bed slope correction term that triggers the instability of the bed [6, 7]
We have shown that the morphodynamic model by Bohorquez & Ancey [10, 11] can be readily generalised to predict the formation of dunes at subcritical flow speed
Summary
The prediction of the occurrence of bedforms and its morphology has been a case of study of great interest due to its influence in major engineering problems such as floods and the effects on the landscape in general. Seems to be a great solution, one of its major drawbacks lies in the huge computational cost that confines its use rather in supercomputers or for a simplified and low-resolution computational domain. Within this strategy, many studies have been carried out, such as Niemann et al [4] and Van Duin et al [5]. Existing morphodynamic models predict the formation of bedforms with precision at the expense of relatively high computational cost or approximately using some ad-hoc formulation of physical processes to trigger the instabilities. The key point is the inclusion of a phase lag between the sediment entrainment rate and the depth-averaged flow velocity, as originally proposed by Cañada-Pereira & Bohorquez [2]
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