[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.
[1] This paper presents a morphodynamic model for free surface flows over bed forms. The model reproduces bed form evolution and migration in a physically based manner. The flow model component of the coupled morphodynamic model, which is twodimensional in the streamwise and vertical directions, explicitly treats unsteadiness and nonhydrostatic effects. Comparison with measurements shows that the flow model accurately simulates both mean flow and turbulence structure induced by bed forms under free surface flow. The flow model performance is enhanced by the use of a high-order Godunov scheme known as the cubic interpolated pseudoparticle (CIP) technique to compute the advection phase of the Navier-Stokes equation. In addition, an enhanced k-e turbulence closure with nonlinear terms is incorporated in the present model in order to allow better predictions of Reynolds stress anisotropy in regions with flow separation. Performance of the nonlinear k-e model is compared with standard k-e closure in the context of the flow as well as morphodynamic simulation. Nonequilibrium bed load sediment transport is treated using a Eulerian stochastic formulation of the sediment exchange process in terms of pickup and deposition functions. The proposed approach for sediment transport explicitly considers the local flow variability during morphodynamic computation. Model results show that the vertical grid distribution pattern affects the simulation result, particularly for bed form morphodymics. The model successfully simulates some important physical features of bed form evolution, such as amalgamation and asymmetric geometry. The simulation results are in agreement with laboratory experiments as well as some commonly used prediction methods for geometric characteristics of bed forms.
Laboratory observations and computational results for the response of bedform fields to rapid variations in discharge are compared and discussed. The simple case considered here begins with a relatively low discharge over a flat bed on which bedforms are initiated, followed by a short high-flow period with double the original discharge, during which the morphology of the bedforms adjusts, followed in turn by a relatively long period of the original low discharge. For the grain size and hydraulic conditions selected, the Froude number remains subcritical during the experiment, and sediment moves predominantly as bedload. Observations show rapid development of quasi-two-dimensional bedforms during the initial period of low flow with increasing wavelength and height over the initial low-flow period. When the flow increases, the bedforms rapidly increase in wavelength and height, as expected from other empirical results. When the flow decreases back to the original discharge, the height of the bedforms quickly decreases in response, but the wavelength decreases much more slowly. Computational results using an unsteady two-dimensional flow model coupled to a disequilibrium bedload transport model for the same conditions simulate the formation and initial growth of the bedforms fairly accurately and also predict an increase in dimensions during the high-flow period. However, the computational model predicts a much slower rate of wavelength increase, and also performs less accurately during the final low-flow period, where the wavelength remains essentially constant, rather than decreasing. In addition, the numerical results show less variability in bedform wavelength and height than the measured values; the bedform shape is also somewhat different. Based on observations, these discrepancies may result from the simplified model for sediment particle step lengths used in the computational approach. Experiments show that the particle step length varies spatially and temporally over the bedforms during the evolution process. Assuming a constant value for the step length neglects the role of flow alterations in the bedload sediment-transport process, which appears to result in predicted bedform wavelength changes smaller than those observed. However, observations also suggest that three-dimensional effects play at least some role in the decrease of bedform wavelength, so incorporating better models for particle hop lengths alone may not be sufficient to improve model predictions.
Results from computational morphodynamics modeling of coupled flow-bed-sediment systems are described for 10 applications as a review of recent advances in the field. Each of these applications is drawn from solvers included in the publicdomain International River Interface Cooperative (iRIC) software package. For mesoscale river features such as bars, predictions of alternate and higher mode river bars are shown for flows with equilibrium sediment supply and for a single case of oversupplied sediment. For microscale bed features such as bedforms, computational results are shown for the development and evolution of two-dimensional bedforms using a simple closure-based two-dimensional model, for two-and three-dimensional ripples and dunes using a three-dimensional large-eddy simulation flow model coupled to a physics-based particle transport model, and for the development of bed streaks using a three-dimensional unsteady Reynolds-averaged Navier-Stokes solver with a simple sedimenttransport treatment. Finally, macroscale or channel evolution treatments are used to examine the temporal development of meandering channels, a failure model for cantilevered banks, the effect of bank vegetation on channel width, the development of channel networks in tidal systems, and the evolution of bedrock channels. In all examples, computational morphodynamics results from iRIC solvers compare well to observations of natural bed morphology. For each of the three scales investigated here, brief suggestions for future work and potential research directions are offered.
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