Numerical simulation of dune–flat bed transition and stage‐discharge relationship with hysteresis effect

Abstract

[1] This work presents recent advances on morphodynamic modeling of bed forms under unsteady discharge. This paper includes further development of a morphodynamic model proposed earlier by Giri and Shimizu (2006a). This model reproduces the temporal development of river dunes and accurately replicates the physical properties associated with bed form evolution. Model results appear to provide accurate predictions of bed form geometry and form drag over bed forms for arbitrary steady flows. However, accurate predictions of temporal changes of form drag are key to the prediction of stage-discharge relation during flood events. Herein, the model capability is extended to replicate the dune-flat bed transition, and in turn, the variation of form drag produced by the temporal growth or decay of bed forms under unsteady flow conditions. Some numerical experiments are performed to analyze hysteresis of the stage-discharge relationship caused by the transition between dune and flat bed regimes during rising and falling stages of varying flows. The numerical model successfully simulates dune-flat bed transition and the associated hysteresis of the stage-discharge relationship; this is in good agreement with physical observations but has been treated in the past only using empirical methods. A hypothetical relationship for a sediment parameter (the mean step length) is proposed to a first level of approximation that enables reproduction of the dune-flat bed transition. The proposed numerical model demonstrates its ability to address an important practical problem associated with bed form evolution and flow resistance in varying flows.

Modelling the transition from dunes to the upper-stage plane bed

“…The main research question of this paper is how to calculate the step length from the hydrodynamic data, so that we can replicate the validation case of Shimizu et al (2009). This validation case is similar to experiments done in flumes.…”

“…The deposition of sediment away from the pick-up point is determined by using a distribution function that relies on the mean step length. This pick-up and deposition model had already been used in the dune evolution model of Shimizu et al (2009), with good results (regarding prediction of dunes and upper-stage plane bed).…”

Computational Modelling of Fluvial Flat Bed Regime

“…This gives rise to another hysteresis effect in the stage-discharge relation during flood events 8),9) . Using the Giri and Shimizu's 10) model for bedform evolution, Shimizu et al 6) were able to reproduce this behaviour. In the experimental study of Shimizu et al 6) , the flume is narrow (10 cm) that two-dimensional dunes are enforced.…”

“…Using the Giri and Shimizu's 10) model for bedform evolution, Shimizu et al 6) were able to reproduce this behaviour. In the experimental study of Shimizu et al 6) , the flume is narrow (10 cm) that two-dimensional dunes are enforced. Moreover, the Giri and Shimizu 10) model is calibrated by adjusting the step length, which reduces its predictive capability.…”

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

“…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].…”