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.

Channel bifurcations are a fundamental element of a broad variety of flowing freshwater environments worldwide, such as braiding and anabranching rivers, river deltas and alluvial fans. River bifurcations often develop asymmetrical configurations with uneven discharge partition and a bed elevation gap between the downstream anabranches. This has been reproduced by one-dimensional (1-D) analytical theories which, however, rely on the empirical calibration of one or more parameters and cannot provide a clear and detailed physical explanation of the observed dynamics. We propose a novel two-dimensional (2-D) solution for the flow and bed topography in channel bifurcations based on an innovative application to a multi-thread channel configuration of the 2-D steady linear solution developed decades ago to study river bars and meandering in single thread river settings. The resonant value of the upstream channel aspect ratio, corresponding to the theoretical resonance condition of regular river meanders (Blondeaux & Seminara, J. Fluid Mech., vol. 157, 1985, pp. 449–470) is the key parameter discriminating between symmetrical and asymmetrical bifurcations, in quantitative agreement with experimental observations and numerical simulations, and qualitatively matching field observations. Only when the aspect ratio of the upstream channel of the bifurcation exceeds resonance, is the bifurcation node able to trigger the upstream development of a steady alternate bar pattern, thus creating an unbalanced configuration. Ultimately, the work provides an analytical explanation of the intrinsic legacy between bifurcation asymmetry and the phenomenon of 2-D upstream morphodynamic influence discovered by Zolezzi & Seminara (J. Fluid Mech., vol. 438, 2001, pp. 183–211).

Two experiments pursued previous studies (P. Viviani & P. Mounoud, 1990; P. Viviani & N. Stucchi, 1989) on motor-perceptual interactions. The right arm of blindfolded participants was moved passively along elliptic trajectories. Kinematics was either coherent or at variance with the relation (two-thirds power law) observed in active movements. In Experiment 1 participants compared the horizontal and vertical extent of the ellipses. Kinematics affected aspect ratio discrimination: The direction along which the movement decelerated was subjectively stretched. In Experiment 2 participants used the left arm to reproduce in real time the movement of the right arm. The trajectories of the left arm presented a stretch similar to the perceptual illusion demonstrated in Experiment 1. Between-arm asynchrony suggests that the motor control system cannot use kinesthetic information that is at variance with the flow of reafferences normally associated with voluntary movements. It is argued that these interactions occur at the level of a central amodal representation of the stimuli.

The study of multithread systems like braided and anastomosing rivers, deltas, alluvial fans, represents a fascinating topic in the vast world of river patterns. The flow splits around exposed bars, islands, ridges, and often reconnects a little further downstream. Water and sediment partition in the bifurcates has a fundamental control of the river morphological evolution and ecological functionality (Ashmore, 2013; Nanson & Knighton, 1996). At the channel scale, bifurcations and confluences play the role of basic unit processes of multithread systems. Understanding their own distinct morphology, flow structure and dynamics, as well as their mutual interplay, is therefore of crucial importance for managing water resources, mitigating the impacts of anthropic pressure [e.g., dams construction (Graf, 2006; Tong-Huan et al., 2020)], ensuring flood protection and adopting river restoration measures suitable for recovering deteriorated ecosystems (e.g., Habersack & Piégay, 2007; Wohl et al., 2015). Almost all studies performed to date consider the two processes separately, although they frequently appear as closely interconnected. Figure 1 shows some illustrative examples of the morphological bond between bifurcations and confluences in different fluvial environments. Braided rivers like the Rakaia River in New Zealand (Figure 1a) are characterized by a complex, highly dynamic planform, where the water and sediment fluxes divide among multiple channels, although just few of them are morphologically active at a given time (Ashmore, 2001; Bertoldi et al., 2009a). In these fluvial systems, sequences of confluence-bifurcation units are ubiquitous features that control channel morphology and the spatial/temporal patterns of sediment transport (Ashmore, 2001; Ashworth, 1996). Midchannels bars and vegetated islands frequently recur in natural meandering rivers (Figure 1b), often associated with width fluctuations or chute and neck cutoff (Grenfell et al., 2012; Zolezzi et al., 2012). They also serve as key elements in the restoration of pristine multithread patterns, as in the case of the Drau River in Austria (Figure 1c), where a former side-channel was reopened with the aim of improving the habitat conditions, stabilize the river bed, and ensure flood protection through channel widening (

Understanding the role of external controls on the morphology of braided rivers is currently limited by the dearth of robust metrics to quantify and distinguish the diversity of channel form. Most existing measures are strongly dependent on river stage and unable to account for the three-dimensional complexity that is apparent in digital terrain models of braided rivers. In this paper, we introduce a simple, stage-independent morphological indicator that enables the analysis of reach-scale regime morphology as a function of slope, discharge, sediment size and degree of confinement. The index is derived from the bed elevation frequency distribution and characterizes a statistical widthdepth curve averaged longitudinally over multiple channel widths. In this way, we define a "synthetic channel" described by a simple parameter that embeds information about the river morphological complexity. Under the assumption of uniform flow, this approach can be extended to provide estimates of the reach-averaged shear stress distribution, bed load flux and at-a-stationvariability of wetted width. We test this approach using data from a wide range of labile channels including 58 flume experiments and three gravel bed braided rivers. Results demonstrate a strong relationship between the unit discharge and the shape of the elevation distribution, which varies between a U-shape for typical single-thread confined channels, to a Y-shape for multithread reaches. Finally, we discuss the use of the metric as a diagnostic index of river condition that may be used to support inferences about the river morphological trajectory.