Modeling river dune evolution using a parameterization of flow separation

Abstract

[1] This paper presents an idealized morphodynamic model to predict river dune evolution. The flow field is solved in a vertical plane assuming hydrostatic pressure conditions. The sediment transport is computed using a Meyer-Peter-Müller type of equation, including gravitational bed slope effects and a critical bed shear stress. To avoid the necessity of modeling the complex flow inside the flow separation zone, we follow an approach similar to one used earlier to simulate the dynamics of wind-blown desert dunes. In case of flow separation, the separation streamline acts as an artificial bed and sediment avalanches down the leeside distributing evenly on the leeside at the angle of repose. Model results show that bed slope effects play a crucial role in the determination of the fastest-growing wavelength from a linear analysis. Flow separation is shown to be crucial to take into account if the dune lee exceeds a certain threshold slope. If flow separation is not included, dune shapes are incorrectly predicted and the dune height saturates at an early stage of bed form evolution, yielding an underprediction of dune height and time to equilibrium. The local bed slope at the dune crest plays a critical role for obtaining an equilibrium dune height. The simulation model is able to predict the main characteristics of dune evolution, such as dune asymmetry, dune growth, and saturation at a certain dune height. Dune dimensions, migration rates, and times to equilibrium compare reasonably well to various data sets.

Morphodynamics of river dunes : suspended sediment transport along mobile dunes and dune development towards upper stage plane bed

“…The mean vertical turbulent flux ' ' c w , along the entire dune bed and in the bed load layer, reaches nearly 30% of the total mean vertical flux cw . The dune evolution model of Paarlberg et al [2009] was used to study the transition of dunes to upper stage plane bed (Chapter 5). This model was extended by including in the model the transport of bed sediment in suspension.…”

“…However, at present, there is no model available that -at operational time scales (time scale of a flood wave) -can describe the dune transition to upper stage plane bed. Paarlberg et al [2009] successfully developed a dune evolution model that is able to predict dune development from small initial disturbances towards fully developed dunes in the lower flow regime. The model's computational time was drastically reduced by using a parameterization of the flow separation zone instead of solving the full hydrodynamic and sediment equations in this turbulent region.…”

“…To study to what extent dune transition to upper stage plane bed can be reproduced with an idealized model, the dune evolution model of Paarlberg et al [2009] was used and extended by including in the model the transport of bed sediment in suspension (Q4). Furthermore, additional flume experiments were carried out to understand the morphological behavior of dunes for a wide range of flow conditions and to investigate the time scales related to the transition of dunes to upper stage plane bed.…”

“…Paarlberg et al [2009] successfully developed a dune evolution model that is able to predict dune development from small initial disturbances towards fully developed dunes in the lower flow regime (bed load dominated regime). The model's computational time was drastically reduced by using a parameterization of the flow separation zone instead of solving the full hydrodynamic and sediment equations in this turbulent region [see Paarlberg et al, 2007].…”

“…Simpler, more efficient dune evolution models exist that calculate the turbulent flow field over dunes or use a parameterization for the flow separation zone in combination with morphodynamic calculations [e.g. Shimizu et al, 2001;Jerolmack and Mohrig, 2005;Nelson et al, 2005;Tjerry and Fredsøe, 2005;Giri and Shimizu, 2006;Paarlberg et al, 2007Paarlberg et al, , 2009Shimizu et al, 2009;Niemann et al, 2011].…”