Riparian ecosystems exhibit complex biotic and abiotic dynamics, where the triad vegetation‐sediments‐stream determines the ecogeomorphological features of the river landscape. Random fluctuations of the water stage are a key trait of this triad, and a number of behaviors of the fluvial environment can be understood only taking into consideration the role of noise. In order to elucidate how randomness shape riparian transects, a stochastic model that takes into account the main links between vegetation, sediments, and the stream is adopted, emphasizing the capability of vegetation to alter the plot topography. A minimalistic approach is pursued, and the probability density function of vegetation biomass is analytically evaluated in any transect plot. This probability density function strongly depends on the vegetation‐topography feedback. We demonstrate how the vegetation‐induced modifications of the bed topography create more suitable conditions for the survival of vegetation in a stochastically dominated environment.

Riparian vegetation is a key element in a number of processes that determine the ecogeomorphological features of the river landscape. Depending on the river water stage fluctuations, vegetation biomass randomly switches between growth and degradation phases and exhibits relevant temporal variations. A full understanding of vegetation dynamics is therefore only possible if the hydrological stochastic forcing is considered. In this vein, we focus on the recovery time of vegetation, namely the typical time taken by vegetation to recover a well‐developed state starting from a low biomass value (induced, for instance, by an intense flood). The analytical expression of the plot‐dependent recovery time is given, the role of hydrological and biological parameters is discussed, and the impact of river‐induced randomness is highlighted. Finally, the effect of man‐induced hydrological changes (e.g., river damming or climate changes) is explored.

Precipitation of calcium carbonate from water films generates fascinating calcite morphologies that have attracted scientific interest over past centuries. Nowadays, speleothems are no longer known only for their beauty but they are also recognized to be precious records of past climatic conditions, and research aims to unveil and understand the mechanisms responsible for their morphological evolution. In this paper, we focus on crenulations, a widely observed ripple-like instability of the the calcite–water interface that develops orthogonally to the film flow. We expand a previous work providing new insights about the chemical and physical mechanisms that drive the formation of crenulations. In particular, we demonstrate the marginal role played by carbon dioxide transport in generating crenulation patterns, which are indeed induced by the hydrodynamic response of the free surface of the water film. Furthermore, we investigate the role of different environmental parameters, such as temperature, concentration of dissolved ions and wall slope. We also assess the convective/absolute nature of the crenulation instability. Finally, the possibility of using crenulation wavelength as a proxy of past flows is briefly discussed from a theoretical point of view.

River dunes and antidunes are induced by the morphological instability of stream-sediment boundary. Such bedforms raise a number of subtle theoretical questions and are crucial for many engineering and environmental problems. Despite their importance, the absolute/convective nature of the instability has never been addressed. The present work fills this gap as we demonstrate, by the cusp map method, that dune instability is convective for all values of the physical control parameters, while the antidune instability exhibits both behaviors. These theoretical predictions explain some previous experimental and numerical observations and are important to correctly plan flume experiments, numerical simulations, paleo-hydraulic reconstructions, and river works.

Film hydrodynamics is crucial in water-driven morphological pattern formation. A prominent example is given by icicle ripples and ice ripples, which are regular patterns developing on freezing-melting inclined surfaces bounding open-channel flows. By a suitable mathematical model based on conservation principles and the use of the cusp map method, in this paper we address the convective-absolute nature of these two kinds of instabilities. The obtained results show that icicle ripples, which develop at inverted (overhang) conditions, have subcentimetric wavelengths which are unstable when the Reynolds number of the liquid flow ($\mathrm{Re}$) is small and the supercooling is intensive. With the increase in $\mathrm{Re}$, the instability switches from absolute to convective. Ice ripples instead exhibit the opposite dependance on $\mathrm{Re}$ and are highly affected by the surface slope. In addition, the evaluation of the so-called absolute wave number, which is responsible for the asymptotic impulse response, suggests a different interpretation of some recent experiments about ice ripples.