.[1] Most morphodynamic models of river meandering assume spatially constant width; depending on the intensity of spatial width variations, different meandering styles actually exist, often associated with midchannel bars and islands. When intense enough, width oscillations characterize transitional planforms between meandering and braiding. We investigate, on a modeling basis, morphodynamic feedbacks between spatial curvature and width oscillations in river meanders and related bedform patterns. Our review of existing mathematical models suggests that width-curvature interactions can be comprehensively analyzed by a hierarchy of models that descend from a two-parameter perturbation solution of the governing depth-averaged morphodynamic model. The focus is on in-stream, autogenic hydromorphodynamic processes, and not explicitly on bank processes. Curvature-width interactions are fundamentally nonlinear: the perturbation approach allows us to investigate the key effects at the first nonlinear interaction. In meanders with initially constant width, curvature nonlinearly forces midchannel bar growth, promoting symmetrical bank erosion further downstream, possibly triggering width oscillations. These in turn can significantly affect the process of bend stability and therefore condition the curvature dynamics. Wider-at-bends meanders develop shorter bends and are morphologically more active compared to equiwidth meanders, coherently with the few available field observations. River evolution models aiming to separately simulate bank erosion and accretion processes should incorporate these autogenic flow-bed nonlinearities. Because of its focus on meandering morphologies close to the transition with braiding, the proposed approach can be taken as a novel, physically based viewpoint to the long-debated subject of channel pattern selection.Citation: Zolezzi, G., R. Luchi, and M. Tubino (2012), Modeling morphodynamic processes in meandering rivers with spatial width variations, Rev. Geophys., 50, RG4005,

[1] Despite the wide spectrum of perturbations of flow and sediment transport experienced by rivers as a result of hydrologic variations, the paradigm of morphodynamic equilibrium has long been present in the geomorphological literature where it is traditionally associated with the semiempirical notion of formative discharge, whereby the unsteady forcing is taken as morphologically equivalent to some effective steady forcing. Here we investigate the mechanisms responsible for maintaining a quasi-equilibrium bed profile of a river reach sufficiently short to have no significant tributary inputs. More importantly, we assume the channel banks to be fixed, hence, the case we have in mind is that of rivers protected by levees which cannot respond to hydrologic forcing by changing their width like natural rivers. Employing a 1-D model of river morphodynamics, we first determine the equilibrium profile of the river reach for given steady forcing conditions and discuss the capability of this approach for interpreting bed profiles observed in the field by applying it to the terminal reach of the Magra River, Italy. Field observations turn out to be reasonably well fitted by the equilibrium profile associated with a steady effective discharge, which however differs from the typical formative discharge (mean annual flood) for natural channels with erodible banks. Finally, we clarify how fluctuations of the hydrodynamic forcing associated with the recorded historical sequence of hydrologic events of variable intensities have acted to maintain the river equilibrium.

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An analytical modelling framework is proposed to reproduce the frequently observed but poorly studied occurrence of mid-channel bars in meandering channels. Mid-channel bars occur in meanders and may characterize transitional morphologies between pure meandering and braided rivers. Based on existing fi eld and experimental observations, we propose that two different mechanisms can generate central topographical patterns in meanders. A former mechanism ('width-forced') is related to spatial width oscillations which determine a laterally symmetrical bed shear stress pattern that promotes mid-channel bars. A second mechanism ('curvature-forced') can take place also in curvilinear equiwidth streams since also longitudinal variations of channel curvature can produce laterally symmetrical alterations of the sediment transport capacity. A perturbation approach is employed to model both mechanisms within a common framework, allowing reproduction, at least qualitatively, of several observed features. While width-forced mid-channel bars are a symmetric linear altimetric response, to reproduce curvature-forced mid-channel bars requires modelling nonlinear fl ow-bed topography interactions at the second order of the perturbation expansion. Hypotheses on how these mechanisms operate are further discussed through an application to fi eld cases. The amplitude of the nonlinear response can be relevant compared to that of the point bar in equiwidth meanders and the location of midchannel bars seldom coincides with bend apexes, mainly depending upon the intrinsic meander wavelength. Central bars tend to symmetrically divert the fl ow against the two banks, a process which is proposed as a possible cause of cross-sectional overwidening, along with the asymmetry between the rates of bank erosion and of the opposite bank accretion. The outcomes of this fi rst modelling step on the subject allow discussion of the mutual feedback processes that characterize interactions between midchannel bars and width variations in river meanders.

The present work revisits the classical, uniform-width bend theory with the aim to understand whether and how spatial width oscillations can affect the process of linear bend stability that initiates meander planform evolution. Although longitudinal oscillations of channel width are common along many meandering streams, little investigation of their properties and dynamic effects has been pursued so far. The theory therefore accounts for width variations as a geometrical forcing in a depth-averaged model of meander morphodynamics by assuming the potential interaction with the classical curvature forcing effect. A first quantification of width variations is made by referring to a freely evolving meandering river, which shows that the dimensionless amplitude of width variations is a ‘small’ parameter with comparable magnitude to that of curvature variations, thus suggesting the use of a two-parameter perturbation expansion. Moreover, it is reasonable to assume that channel width oscillates in space with a double frequency relative to curvature, which implies that one nonlinear interaction between the two forcing effects is enough to reproduce the effect of spatial width variations on the process of bend stability. Overall, width variations consistently promote the instability of shorter bends with respect to meanders with uniform width: on average, this predicted tendency is supported by analysis of field data referring to hundreds of natural meander bends. The effect on meander wavelength selection depends on the location of the widest section relative to the bend apex. Under typical formative conditions of gravel-bed rivers, with large-enough channel aspect ratios, two distinct most unstable longitudinal modes develop. Such behaviour is absent when the width is uniform, and suggests a mechanistic interpretation for the reach-scale occurrence of chute cutoffs that can be observed more frequently in wider-at-bends than in equiwidth meandering channels.