[1] In the present contribution we focus our attention on the long-term behavior of meandering rivers, a very common pattern in nature. This class of dynamical systems is driven by the coexistence of various intrinsically nonlinear mechanisms which determine the possible occurrence of two different morphodynamic regimes: the subresonant and the superresonant regimes. Investigating the full range of morphodynamic conditions, we objectively compare the morphologic characteristics exhibited by synthetically generated and observed planimetric patterns. The analysis is carried out examining, through principal component analysis, a suitable set of morphological variables. We show that even in the presence of the strong filtering action exerted by cutoff processes, a closer, although not yet complete, similarity with natural meandering planforms can be achieved only by adopting a flow field model which accounts for the full range of morphodynamic regimes. We also introduce a new morphodynamic length scale, L m , associated with spatially oscillating disturbances. Once normalized with this length scale, the relevant morphologic features of the simulated long-term patterns (e.g., the probability density function of local curvature and the geometric characteristics of oxbow lakes) tend to collapse on two distinct behaviors, depending on the dominant morphologic regime.

[1] Like most media, open channel flows propagate information through waves. When the channel boundary is fixed, the vectors of information consist typically of surface gravity waves. In the less straightforward case of channels with cohesionless bed and possibly erodible banks, other types of waves arise from the erodible nature of the boundaries and the ability of the stream to transport sediments. In this paper we restrict our attention to the important case of long waves, which can be described by employing the shallow water approximation for the flow field and a quasi-equilibrium assumption for sediment transport on weakly sloping beds. We focus on a major issue: In which direction is information propagated? This is a problem raised and partially solved by de Vries in the context of one-dimensional morphological modeling as early as 1965. We review some of the available knowledge on this subject, viewed in a more general context where vectors of information can be a variety of waves: purely longitudinal onedimensional sediment waves, two-dimensional waves driven by large-scale bed forms (bars), and plan form waves carrying information related to the planform shape of the channel. Both linear and nonlinear, migrating and stationary waves are considered. It turns out that the role played by the Froude number in determining the direction of one-dimensional perturbations of bed topography is somewhat taken by the aspect ratio of the channel when large-scale two-dimensional bed forms as well as planform waves are considered.

In the present contribution we focus our attention on the possible signatures of a chaotic behaviour or a selforganized criticality state triggered in river meandering dynamics by repeated occurrence of cutoff processes. The analysis is carried out examining, through some robust nonlinear methodologies inferred from time series analysis, both the spatial series of local curvatures and the time series of long-term channel sinuosity. Temporal distribution of cutoff inter-arrivals is also investigated. The analyzed data have been obtained by using a suitable physics-based simulation model for river meandering able to reproduce reasonably the features of real rivers. The results are consistent and show that, at least from a modelling point of view, no evidence of chaotic determinism or self-organized criticality is detectable in the investigated meandering dynamics.

High‐resolution bathymetry, seismic reflection, and piston core data from a submarine channel on the western Niger Delta slope demonstrate that thick, coarse‐grained, amalgamated sands in the channel thalweg/axis transition to thin, fine‐grained, bedded sands and muds in the channel margin. Radiocarbon ages indicate that axis and margin deposits are coeval. Core data show that bed thickness, grain size, and deposition rate strongly decrease with increasing height above channel thalweg and/or distance from channel centerline. A 5 times decrease in bed thickness and 1–2 ψ decrease in grain size are evident over a 20 m elevation change (approximately the elevation difference between axis and margin). A simplified in‐channel sedimentation model that solves vertical concentration and velocity profiles of turbidity currents accurately reproduces the vertical trends in grain size and bed thickness shown in the core data set. The close match between data and model suggests that the vertical distribution of grain size and bed thickness shown in this study is widely applicable and can be used to predict grain size and facies variation in data‐poor areas (e.g., subsurface cores). This study emphasizes that facies models for submarine channel deposits should recognize that grain‐size and thickness trends within contemporaneous axis‐margin packages require a change in elevation above the thalweg. The transition from thick‐bedded, amalgamated, coarser‐grained sands to thin‐bedded, nonamalgamated, finer‐grained successions is primarily a reflection of a change in elevation. Even a relatively small elevation change (e.g., 1 m) is enough to result in a significant change in grain size, bed thickness, and facies.

[1] The mathematical modeling of the long-term evolution of meandering rivers needs an efficient computation of the flow field. Indeed, the estimate of the near bank velocity, needed to determine the rate at which the outer bank migrates, cannot rely on the full numerical solution of the governing equations when considering the river evolution on geological time scales. The aim of the present contribution is twofold: determining the complete linear response of a meandering river to spatially varying channel axis curvature and width, exploiting the ability of the model to describe the morphological tendencies of alluvial rivers; and developing a computationally efficient tool that can be easily incorporated in long-term planform evolution models. The centrifugally induced secondary flow associated with channel axis curvature and longitudinal convection is accounted for by a suitable parametrization based on the structure of the three-dimensional flow field. Cross section width variations are accounted for through a suitable stretching of the transverse coordinate. The relevant momentum and mass conservation equations are then linearized by taking advantage of the fact that alluvial rivers often exhibit mild and long meander bends, as well as evident but relatively small width variations. The input data needed by the analytical solution are the spatial distribution of channel axis curvature and width variations, the mean slope of the investigated river reach, the characteristic grain size of the sediment bed and the flow discharge. The performances of the model, as well as its intrinsic limitations are discussed with reference to the comparison with the bed topography surveyed in a 21 km long reach of the Po River. The results indicate that, in the presence of wide, mildly curved and long bend and weak width variations, the river topography is described with a good accuracy, thus supporting the use of the model to investigate how a river could react to changes in planform geometry or external forcing. Moreover, the analytical character of the model implies a limited computational effort, facilitating a straightforward integration within the models used to simulate the planimetric evolution of alluvial rivers on geological time scales.Citation: Frascati, A., and S. Lanzoni (2013), A mathematical model for meandering rivers with varying width,