Many models of river meander migration rely upon a simple formalism, whereby the eroding bank is cut back at a rate that is dictated by the flow, and the depositing bank then migrates passively in response, so as to maintain a constant bankfull channel width. Here a new model is presented, in which separate relations are developed for the migration of the eroding bank and the depositing bank. It is assumed that the eroding bank consists of a layer of fine-grained sediment that is cohesive and/or densely riddled with roots, underlain by a purely noncohesive layer of sand and/or gravel. Following erosion of the noncohesive layer, the cohesive layer fails in the form of slump blocks, which armor the noncohesive layer and thereby moderate the erosion rate. If the slump block material breaks down or is fluvially entrained, the protection it provides for the noncohesive layer diminishes and bank erosion is renewed. Renewed bank erosion, however, rejuvenates slump block armoring. At the depositing bank, it is assumed that all the sediment delivered to the edge of vegetation due to the transverse component of sediment transport is captured by encroaching vegetation, which is not removed by successive floods. Separate equations describing the migration of the eroding and depositing banks are tied to a standard morphodynamic formulation for the evolution of the flow and bed in the central region of the channel. In this model, the river evolves toward maintenance of roughly constant bankfull width as it migrates only to the extent that the eroding bank and depositing bank 'talk' to each other via the medium of the morphodynamics of the channel center region. The model allows for both (a) migration for which erosion widens the channel, forcing deposition at the opposite bank, and (b) migration for which deposition narrows the channel forcing erosion at the opposite bank.

A major control on bedrock incision is the interaction between alluvial cover and erosive mobile grains. The extent of alluvial cover is typically predicted as a function of relative sediment flux (sediment supply rate over bed load transport capacity, q bs /q bc ), yet little is known about how the bed roughness affects the alluvial cover. We performed field experiments with various flow discharges, sediment supply rates, grain sizes, and bed surface topographies. We then developed physically based models for estimating the threshold of sediment movement and the extent of alluvial cover, so as to include the effect of roughness change. The results for the threshold of sediment movement and the extent of alluvial cover obtained from our models show reasonable agreement with the results of the field experiments. We explored the sensitivity of the models to variations in sediment supply and bedrock relative roughness (bedrock hydraulic roughness height over grain size, k sb /d). The results suggest the following: (1) a larger relative roughness yields a greater dimensionless critical shear stress required for initial sediment motion; (2) at a given sediment supply rate, the extent of alluvial cover is larger when the relative roughness is larger; (3) when the sediment supply rate and the relative roughness are small, throughput bed load moves over (and can abrade) a purely bedrock channel with no alluvial cover; and (4) the critical value of sediment supply rate below which throughput bed load transport occurs increases with decreasing relative roughness. The experimental results and analysis provide a framework for treating the (a) incisional morphodynamics of purely bedrock rivers by throughput bed load with no alluvial cover, (b) incisional/alluvial morphodynamics of mixed bedrock-alluvial rivers, and (c) purely alluvial morphodynamics, as well as the transition between these states.

[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.

Meandering rivers display active communication between bank erosion and bar deposition processes. How does this occur? How does the river select its width? To answer these questions, we implement a model for meander migration where both bank processes (erosion and deposition) are considered independently. Bank erosion is modeled as erosion of purely noncohesive bank material damped by natural slump block armoring; channel deposition is modeled via flow-retarded vegetal encroachment. Both processes are tied to a slope-dependent channel forming Shields number; banks with near-bank Shields number below this value undergo deposition, and those above it undergo erosion. Channel-forming Shields number must increase with slope, as dictated by available data and model performance. Straight channel modeling shows that a channel arrives at an equilibrium width from any initial condition. For the channel bend, the river always approaches an asymptotic state where width reduces slowly in time and where bank erosion and deposition occur at nearly equal rates. Before this state is reached, however, the river follows a phase-plane trajectory with four possible regimes: (a) both banks erode, (b) both banks deposit, (c) both banks migrate outward, but with a faster depositing bank (bar push), and (d) both banks migrate outward, but with a faster eroding bank (bank pull). The trajectory of migration on the phase plane depends on initial conditions and input parameters controlling the rate of depositional and erosional migration. All input parameters have specific physical meaning, and the potential to be measured in the field.

[1] In this study, the natural process of river meandering is captured in a computational model that considers the effects of bank erosion, the process of land accretion along the inner banks of meander bends, and the formation of channel cutoffs. The methodology for predicting bank erosion explicitly includes a submodel treating the formation and eventual removal of slump blocks. The accretion of bank material on the inner bank is modeled by defining the time scale over which areas that are originally channel become land. Channel cutoff formation is treated relatively simply by recomputing the channel alignment at a single model time step when migrating banks meet. The model is used to compute meandering processes in both steady and unsteady flows. The key features of this new model are the ability (a) to describe bank depositional and bank erosional responses separately, (b) to couple them to bed morphodynamics, and thus (c) to describe coevolving river width and sinuosity. Two cases of steady flow are considered, one with a larger discharge (i.e., "bankfull") and one with a smaller discharge (i.e., "low flow"). In the former case, the shear stress is well above the critical shear stress, but in the latter case, it is initially below it. In at least one case of constant discharge, the planform pattern can develop some sinuosity, but the pattern appears to deviate somewhat from that observed in natural meandering channels. For the case of unsteady flow, discharge variation is modeled in the simplest possible manner by cyclically alternating the two discharges used in the steady flow computations. This model produces a rich pattern of meander planform evolution that is consistent with that observed in natural rivers. Also, the relationship between the meandering evolution and the return time scale of floods is investigated by the model under the several unsteady flow patterns. The results indicate that meandering planforms have different shapes depending on the values of these two scales. In predicting meander evolution, it is important to consider the ratio of these two time scales in addition to such factors as bank erosion, slump block formation and decay, bar accretion, and cutoff formation, which are also included in the model.

[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.

A two-dimensional numerical model was developed to simulate relatively wide, shallow rivers with an erodible bed and banks composed of well-sorted, sandy materials. A moving boundary-fitted coordinate system was used to calculate water flow, bed change, and bank erosion. The cubic interpolated pseudoparticle method was used to calculate flow, which introduced little numerical diffusion. The sediment-transport equation for the streamline and transverse transport was used to estimate bed and bank evolution over time, while considering the secondary flow. Bank erosion was simulated when the gradient in the cross-sectional direction of the banks was steeper than the submerged angle of repose because of bed erosion near the banks. The numerical model reproduced the features of central bars well, such as bar growth, channel widening due to divergence of the flow around the bars, scour holes at the lee of the bars, and the increase of bar size with time. These features were in accordance with the observations for laboratory experiments. It also reproduced the features of braided rivers, such as the generation of new channels and abandonment of old channels, the bifurcation and confluence of channels, and the lateral migration of the channels. The model showed that the sediment discharge rate fluctuated with time, one of the dynamic features observed in braided channels.

No abstract