The study of river‐riparian vegetation interactions is an important and intriguing research field in geophysics. Vegetation is an active element of the ecological dynamics of a floodplain which interacts with the fluvial processes and affects the flow field, sediment transport, and the morphology of the river. In turn, the river provides water, sediments, nutrients, and seeds to the nearby riparian vegetation, depending on the hydrological, hydraulic, and geomorphological characteristic of the stream. In the past, the study of this complex theme was approached in two different ways. On the one hand, the subject was faced from a mainly qualitative point of view by ecologists and biogeographers. Riparian vegetation dynamics and its spatial patterns have been described and demonstrated in detail, and the key role of several fluvial processes has been shown, but no mathematical models have been proposed. On the other hand, the quantitative approach to fluvial processes, which is typical of engineers, has led to the development of several morphodynamic models. However, the biological aspect has usually been neglected, and vegetation has only been considered as a static element. In recent years, different scientific communities (ranging from ecologists to biogeographers and from geomorphologists to hydrologists and fluvial engineers) have begun to collaborate and have proposed both semiquantitative and quantitative models of river‐vegetation interconnections. These models demonstrate the importance of linking fluvial morphodynamics and riparian vegetation dynamics to understand the key processes that regulate a riparian environment in order to foresee the impact of anthropogenic actions and to carefully manage and rehabilitate riparian areas. In the first part of this work, we review the main interactions between rivers and riparian vegetation, and their possible modeling. In the second part, we discuss the semiquantitative and quantitative models which have been proposed to date, considering both multi‐ and single‐thread rivers.

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.

A model for the evaluation of the intra‐meander hyporheic exchange fluxes is presented. The method relies on a physically‐based morphodynamic model to predict the characteristics of the flow field in a meandering river and the temporal evolution of its planimetry. The hyporheic fluxes induced at the meander scale by the river sinuosity can therefore be computed. The application of the model to a simulated case has shown the fundamental role of the river planimetry on the hyporheic exchange pattern at the meander scale, and its influence on the long‐term evolution of the hyporheic exchange.

A river and its surrounding riparian vegetation are two dynamical systems that interact through several hydrological, geomorphological, and ecological processes. This work focuses on the role played by vegetation on meandering river morphodynamics: River planform evolution forces the riparian vegetation dynamics, which, in turn, affect the mechanical characteristics of the river banks and influence the meandering dynamics of the river itself. It follows that despite the fact that a traditional engineering approach considers vegetation as a static element the study of river morphodynamics should be coupled with the riparian vegetation evolution. To this end, a fluid dynamic model of meandering rivers is here coupled with a process‐based model for the riparian biomass dynamics. The feedback of vegetation on river morphology is provided by a relation that links the biomass density to the bank erodibility. The numerical results highlight (1) the remarkable effects of the vegetation dynamics on meander evolution and (2) the role of the temporal scales of vegetation growth and decay in relation to typical morphodynamic scales. In particular, the differences with respect to the constant erodibility case can be of the order of tens or hundreds of meters (10–20% of the meander wavelength), and peculiar meander shapes that do not show the usual marked upstream skewness emerge.

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.

Riparian vegetation is part of one of the most diverse and fragile ecotones. The key role played by river discharge on the dynamics of riparian vegetation has been widely studied and documented. However, although randomness is a fundamental characteristic of river hydrology, very few quantitative vegetation studies take into account the random nature of river discharge. Here we propose a stochastic model of riparian vegetation ecosystem dynamics forced by random variations in river discharge. The model is solved, and the analytical expressions of the probability density function of the overall vegetation biomass and its first moments are obtained. These theoretical results are used to investigate the effect of river hydrology on the distribution of vegetation along the riparian transect transverse to the river. In particular, the influence of the type of riparian species and the statistical characteristics of discharge time series are discussed and compared with field observations.