We review the importance of the physical mechanisms involved in river meandering by comparing some existing linear models and extensions thereof. Such models are hierarchically derived from a common and general mathematical framework and then analyzed with a detailed discussion of the physical processes and relevant hypotheses that are involved. Experiments and field data are also used to discuss the related morphodynamic processes. The analysis of the models shows the importance of the closure of secondary currents especially in the modeling of eddy viscosity. This aspect confirms the usefulness of using simplified models for some practical applications, provided the secondary currents are modeled in detail. On the other hand, the free response of the sediments, the phase lag of secondary currents, and the momentum redistribution due to the coupling between the main and the transverse flow are shown to be less relevant. Hence the second‐order models, which neglect the effect of superelevation induced by the topography‐driven lateral flow on the longitudinal flow, can reasonably be considered a good approximation for both predictive analysis and the computation of the resonant conditions. Finally, the analysis of higher harmonics suggests that the multilobed pattern can intrinsically be present in both second‐ and fourth‐order models.

In spite of notable advances in the description of river morphodynamics, the long‐term dynamics of meandering rivers is still an open question, in particular, regarding the existence of a possible statistical steady state and its scaling properties induced by the competing action of cutoffs and reach elongation. By means of extensive numerical simulations, using three fluid dynamic models of different complexity and analysis of real data from the Amazon, North America, and Russia, we show that the reach cutoffs, besides providing stability and self‐confinement to the meander belt, also act as a dynamical filter on several hydrodynamic mechanisms, selecting only those that really dominate the long‐term dynamics. The results show that the long‐term equilibrium conditions are essentially governed by only one spatial scale (proportional to the ratio of the river depth and the friction coefficient) and one temporal scale (proportional to the square of the spatial scale divided by the river width, the mean longitudinal velocity, and the erodibility coefficient) that contain the most important fluid dynamic quantities. The ensuing statistical long‐term behavior of meandering rivers proves to be universal and largely unaffected by the details of the fluid dynamic processes that govern the short‐term river behavior.

The establishment of riparian pioneer vegetation is of crucial importance within river restoration projects. After germination or vegetative reproduction on river bars juvenile plants are often exposed to mortality by uprooting caused by floods. At later stages of root development vegetation uprooting by flow is seen to occur as a consequence of a marked erosion gradually exposing the root system and accordingly reducing the mechanical anchoring. How time scales of flow-induced uprooting do depend on vegetation stages growing in alluvial non-cohesive sediment is currently an open question that we conceptually address in this work. After reviewing vegetation root issues in relation to morphodynamic processes, we then propose two modelling mechanisms (Type I and Type II), respectively concerning the uprooting time scales of early germinated and of mature vegetation. Type I is a purely flow-induced drag mechanism, which causes alone a nearly instantaneous uprooting when exceeding root resistance. Type II arises as a combination of substantial sediment erosion exposing the root system and resulting in a decreased anchoring resistance, eventually degenerating into a Type I mechanism. We support our conceptual models with some preliminary experimental data and discuss the importance of better understanding such mechanisms in order to formulate sounding mathematical models that are suitable to plan and to manage river restoration projects.