[1] The number of bars that form in an alluvial channel cross section can be determined from a physics-based linear model for alluvial bed topography. The classical approach defines separators between ranges in which river planform styles with certain numbers of bars are linearly stable and linearly unstable. We propose an alternative method that is easier to apply. Instead of defining separators between stable and unstable conditions for certain river planform styles, the method directly estimates the most likely number of bars. It is based on a demonstration that conditions of zero spatial damping in a linear model for steady bars are representative for the bar mode that develops inside a river channel. We argue that a method based on steady bars is more appropriate for real rivers than a method based on free migrating bars. We verified the method by applying it to several existing rivers at bankfull conditions. The results are good for width-to-depth ratios up to 100 but deteriorate for higher width-to-depth ratios. We explain the deficiencies for large width-to-depth ratios from the linearity of the model. The results show that our method can be used as a reliable predictor for whether reducing or enlarging the width of a river will lead to a meandering, transition, or braided planform.Citation: Crosato, A., and E. Mosselman (2009), Simple physics-based predictor for the number of river bars and the transition between meandering and braiding, Water Resour. Res., 45, W03424,

The presence of vegetation modifies flow and sediment transport in alluvial channels and hence the morphological evolution of river systems. Plants increase the local roughness, modify flow patterns and provide additional drag, decreasing the bed-shear stress and enhancing local sediment deposition. For this, it is important to take into account the presence of vegetation in morphodynamic modelling. Models describing the effects of vegetation on water flow and sediment transport already exist, but comparative analyses and validations on extensive datasets are still lacking. In order to provide practical information for modelling purposes, we analysed the performance of a large number of models on flow resistance, vegetation drag, vertical velocity profiles and bed-shear stresses in vegetated channels. Their assessments and applicability ranges are derived by comparing their predictions with measured values from a large dataset for different types of submerged and emergent vegetation gathered from the literature. The work includes assessing the performance of the sediment transport capacity formulae of Engelund and Hansen and van Rijn in the case of vegetated beds, as well as the value of the drag coefficient to be used for different types of vegetation and hydraulic conditions. The results provide a unique comparative overview of existing models for the assessment of the effects of vegetation on morphodynamics, highlighting their performances and applicability ranges.

The effects of floodplain vegetation on river planform have been investigated for a medium-sized river using a 2D morphodynamic model with submodels for flow resistance and plant colonization. The flow resistance was divided into a resistance exerted by the soil and a resistance exerted by the plants. In this way it was possible to reproduce both the decrease in bed shear stress, reducing the sediment transport capacity of the flow within the plants, and the increase in hydraulic resistance, reducing the flow velocities. Colonization by plants was obtained by instantaneously assigning vegetation to the areas that became dry at low water stages. This colonization presents a step forward in the modelling of bank accretion. Bank erosion was related to bed degradation at adjacent wet cells. Bank advance and retreat were reproduced as drying and wetting of the computational cells at the channel margins. The model was applied to a hypothetical case with the same characteristics as the Allier River (France). The river was allowed to develop its own geometry starting from a straight, uniform, channel. Different vegetation densities produced different planforms. With bare floodplains, the river always developed a braided planform, even if the discharge was constant and below bankfull. With the highest vegetation density (grass) the flow concentrated in a single channel and formed incipient meanders. Lower vegetation density (pioneer vegetation) led to a transitional planform, with a low degree of braiding and distinguishable incipient meanders. The results comply with flume experiments and field observations reported in the literature.

[1] Alternate bars in straight alluvial channels are migrating or nonmigrating. The currently accepted view is that they are nonmigrating if the width-to-depth ratio is at the value of resonance or if the bars are forced by a persistent local perturbation. We carried out 2-D numerical computations and a long-duration mobile-bed flume experiment to investigate this view. We find that nonmigrating bars can also occur in straight channels without resonant width-to-depth ratio or steady local perturbation. They appear to be an intrinsic response of the alluvial river bed. This finding bears on explanations for meandering of alluvial rivers, for which nonmigrating bars are seen as a prerequisite. We find, however, that the intrinsic tendency of a straight channel to form meanders usually has a different origin. The identified intrinsic nonmigrating bars can only become the dominant mechanism for incipient meandering if the erodibility of the banks is very low.

From an analysis of a time-dependent 2-D model for river bed topography, results are obtained which deepen the understanding of the processes of river bed deformation.With a non-steady state analysis the occurrence and behavior of propagating alternate bars are described.Due to the relatively large propagation velocity of these bars, this type of bed perturbation cannot give an explanation for the much more steady meandering process, which is characterized by the point bar-pool configuration.A steady state analysis turns out to be more appropriate to describe the meandering process.In terms of wave length and longitudinal damping rate, this analysis provides a good description of the phenomena involved.For conditions prevailing in meandering rivers. it appears that the result of the interaction between water and sediment motion depends on the ratio of two characteristic adaptation lengths which govern the two independent equations for the flow and for the bed deformation, respectively. In addition, it is shown that the degree of non-linearity of the sediment transport with flow velocity is also an important parameter.Finally, the results of the analysis are compared with data from a straight flume experiment with movable bed, in which at the inflow a steady perturbation was imposed, and with data from a curved flume experiment with movable bed and fixed banks.

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[1] Migrating alternate bars form in alluvial channels as a result of morphodynamic instability. Extensive literature can be found on their origin and short-term development, but their long-term evolution has been poorly studied so far. In particular, it is not clear whether migrating bars eventually reach a (dynamic) equilibrium, as in previous studies bars were observed to elongate with time. We studied the long-term evolution of alternate bars by performing two independent long-duration laboratory experiments and some numerical tests with a physics-based depth-averaged model. In a straight flume with constant water flow and sediment recirculation, migrating bars followed a cyclic variation. They became gradually longer and higher for a while, then quickly much shorter and lower. In one case, all migrating bars simultaneously vanished almost completely only to reform soon after. At the same time, steady bars, two to three times as long, progressively developed from upstream, gradually suppressing the migrating bars. We also observed simultaneous vanishing of migrating bars in an annular flume experiment, this time at intervals of 6-8 d. Numerical simulations of long alluvial channels with constant flow rate and fixed banks show periodic vanishing of a few migrating bars at a time, occurring at regular spacing. Under constant flow rates, migrating bars appear as a transition phenomenon of alluvial channels having a cyclic character. These observations, however, might hold only for certain morphodynamics conditions, which should be further investigated.

[1] Meander migration models include an as yet poorly investigated source of numerical errors related to the computation of the channel curvature, which are amplified by the procedure of adding and deleting grid points as the river planform evolves. The methods adopted to reduce these errors may influence size, form, and migration rate of the developing meanders, which creates uncertainties in the analysis of the results, limits the model applicability, and makes it necessary to treat the bank erodibility coefficients as calibration parameters. This becomes evident from a series of computational tests performed in order to compare two different methods of error reduction in the computed local channel curvature: cubic spline interpolations versus different levels of curvature smoothing. Since the problems discussed are common to most meander migration models, the tests performed were carried out for three models of different complexity. These were derived by applying different degrees of simplification to the basic equations for water flow and sediment motion of shallow curved channels.