Following ideas developed in the field of hydrodynamic stability of laminar flows (Stuart 1971) a predictive theory is proposed to determine the development of finite-amplitude alternate bars in straight channels with erodible bottoms. It is shown that an ‘equilibrium amplitude’ of bedforms is reached as t → ∞ within a wide range of values of the parameter (β − βc)/βc, where t is the time, β is the width ratio of the channel and βc is its ‘critical’ value below which bars would not form. The theory leads to relationships for the maximum height and the maximum scour of bars which compare satisfactorily with the experimental data of various authors. Moreover the experimentally detected tendency of the bed perturbation to form diagonal fronts is qualitatively reproduced.

[1] We investigate the equilibrium configurations and the stability of river bifurcations in gravel braided networks. Within the context of a one-dimensional approach, the nodal point conditions play a crucial rule, as pointed out by Wang et al. [1995] who propose an empirical relationship relating water and sediment flow rates into the downstream branches. In the present paper, an alternative formulation of nodal point conditions is proposed based on a quasi two-dimensional approach. The results show that, if the Shields parameter of the upstream channel is large enough, the system only admits of one solution with both branches open, which is invariably stable. As the Shields parameter of the upstream channel decreases, two further stable solutions appear characterized by a different partition of water discharge into the downstream branches: in this case, the previous solution becomes unstable. Theoretical findings are confirmed by the numerical solution of the nonlinear onedimensional equations.

The exact solution of the problem of river morphodynamics derived in Part 1 is employed to formulate and solve the problem of planimetric evolution of river meanders. A nonlinear integrodifferential evolution equation in intrinsic coordinates is derived. An exact periodic solution of such an equation is then obtained in terms of a modified Fourier series expansion such that the wavenumbers of the various Fourier modes are time dependent. The amplitudes of the Fourier modes and their wavenumbers satisfy a nonlinear system of coupled ordinary differential equations of the Landau type. Solutions of this system display the occurrence of two possible scenarios. In the sub-resonant regime, i.e. when the aspect ratio of the channel is smaller than the resonant value, meandering evolves according to the classical picture: a periodic train of small-amplitude sine-generated meanders migrating downstream evolve into the classical, upstream skewed, train of meanders of Kinoshita type. Evolution displays all the experimentally observed features: the meander growth rate increases up to a maximum and then decreases, while the migration speed decreases monotonically. No equilibrium solutions are found. In the super-resonant regime the picture is essentially reversed: downstream skewing develops while meanders migrate upstream.Numerical solutions of the planimetric evolution equation are obtained for the case when the initial channel pattern exhibits random small perturbations of the straight configuration. Under these conditions, the evolution displays the typical features of solutions of the Ginzburg–Landau equation, in particular, the occurrence of spatial modulations of the meandering pattern which organizes itself in the form of wavegroups. Furthermore, multiple loops develop in the advanced stage of meander growth.

[1] In this work we have investigated the equilibrium configurations of a Y-shaped fluvial bifurcation through a laboratory analysis. Three series of experimental runs have been performed in a wide flume, where a symmetrical bifurcation has been constructed joining three branches with fixed banks and movable bed made of a well sorted quartz sand; the angle between the two downstream distributaries was equal to 30 degrees. The experiments have been carried out with different values of longitudinal bed slope and water discharge, in order to investigate a range of the relevant morphodynamic parameters typical of gravel bed braided rivers. The equilibrium configuration of the bifurcation has been characterized through the measure of the discharge partition in downstream branches and of the local bed structure at the node. The existence of unbalanced equilibrium configurations has been observed and the role of migrating alternate bars has been pointed out. The experimental results confirm the theoretical predictions which have been recently obtained through the simple model of Bolla Pittaluga et al. (2003). Moreover, interpreting the measured data in the light of the concept of morphodynamic influence provides a new perspective in the analysis of the equilibrium configurations of a bifurcation.

We study the steady three-dimensional flow field and bed topography in a channel with sinusoidally varying width, under the assumptions of small-amplitude width variations and sufficiently wide channel to neglect nonlinear effects and sidewall effects. The aim of the work is to investigate the role of width variations in producing channel bifurcation in braided rivers. We infer incipient bifurcation in cases where the growth of a central bar leads to planimetric instability of the channel, i.e. when the given infinitesimal width perturbation is enhanced. Results of the three-dimensional model suggest that the equilibrium bottom profile mainly consists of a purely longitudinal component, uniformly distributed over the cross-section, which induces deposition at the wide section and scour at the constriction, and of a transverse component in the form of a central bar (wide sections) and scour (constrictions), with longitudinal wavelength equal to that of width variations. A comparison between the results of the three-dimensional model and those obtained by means of a two-dimensional depth-averaged approach shows that the transverse component is mainly related to three-dimensional effects. Theoretical findings display a satisfactory agreement with results of flume experiments. Transverse variations are responsible for the planimetric instability of the channel; we find that in the range of values of Shields stress typical of braided rivers, the incipient bifurcation is enhanced as the width ratio of the channel increases

The high dynamism and complexity of braided networks poses a series of open questions, significant for river restoration and management. The present work is aimed at the characterization of the morphology of braided streams, in order to assess whether the system reaches a steady state under constant flow conditions and, in that case, to determine how it can be described and on which parameters it depends. A series of 14 experimental runs were performed in a laboratory physical model with uniform sand, varying the discharge and the longitudinal slope. Planimetric and altimetric configurations were monitored in order to assess the occurrence of a steady state. A set of parameters was considered, such as the braid-plain width and the number and typology of branches and nodes. Results point out that a relationship exists between braiding morphology and two dimensionless parameters, related to total water discharge and stream power. We found that network complexity increases at higher values of water discharge and a larger portion of branches exhibits morphological activity. Results are then compared to the outputs of a simple one-dimensional model, that allows to easily predict the average network complexity, once the bed topography is known. Model computations permit also the investigation of the effect of water discharge variations and to compare different width definitions. The at-a-station variability of planimetric parameters shows a peculiar behaviour, both regarding number of branches and wetted width. In particular, the analysis of the relationship between width and discharge highlighted relevant differences in comparison to single thread channel. Figure 4. Quantification of the network steady state configuration: A) total braiding index TBI as a function of the dimensionless water discharge; B) total braiding index TBI as a function of the dimensionless stream power index; C) active braiding index ABI as a function of the dimensionless water discharge; D) active braiding index ABI as a function of the dimensionless stream power index.Figure 7. Comparison between the measured values of the total and active braiding indexes and values computed by the 1D numerical model, as a function of the dimensionless discharge and stream power.Figure 8. At-a-station variability of TBI and ABI, as computed by the numerical 1D model. Black dots represent the formative conditions.

Water and sediment distribution by river bifurcations is often highly unbalanced. This may result from a variety of factors, such as migration of bars, channel curvature and backwater effects, which promote an uneven partition of flow and sediment fluxes in the downstream branches, which we call ‘forcings’. Bifurcations also display an intrinsic instability mechanism that leads to unbalanced configurations, as occurs in the idealized case of a geometrically symmetric bifurcation, which we call ‘free’, provided the width‐to‐depth ratio of the incoming flow is large enough. Most frequently, these free and forced mechanisms coexist; however, their controlling roles in bifurcation dynamics have not been investigated so far. In this paper we address this question by proposing a unified free‐forced modelling framework for bifurcation morphodynamics. Upstream channel curvature and different slopes of downstream branches (slope advantage) are specifically investigated as forcing effects typically occurring in bifurcations of alluvial channels. The modelling strategy is based on the widely used two‐cell model of Bolla Pittaluga et al. (Water Resources Research, 2003, 39(3), 1–13), here extended to account for the spatially non‐uniform fluxes entering the bifurcation node. Results reveal that the relative role of free and forced mechanisms depends on the width‐to‐depth ratio falling above or below the resonant threshold that controls the stability of free bifurcations: when the main channel is relatively wide and shallow (super‐resonant regime) the bifurcation invariably evolves towards unbalanced configurations, whatever the combination of curvature and slope advantage values, which instead control the bifurcation response under sub‐resonant conditions. Detection of the resonant aspect ratio as a key threshold also releases the modelling approach from the need for parameter calibration that characterized previous approaches, and allows for interpreting under a unified framework the opposite behaviours shown by gravel‐bed and sand‐bed bifurcations for increasing Shields parameter values. © 2018 John Wiley & Sons, Ltd.

In the paper we review some recent work on the mechanics of formation and development of river bars. The emphasis is placed on the instability process which leads to the spontaneous development of bars in almost straight reaches of alluvial rivers. A three dimensional formulation of the problem is presented along with a discussion on the relevant closure relationships. Results of linear and non linear theories for free bars under bedload dominated conditions are summarised. Furthermore, account is given on the effect on bar instability induced by suspended load, grain sorting and width variations. Some as yet unpublished results are also presented