River antidunes and bars: new models and nonmodal analysis

The first part of this thesis deals with river alternate bars. Fluvial bars are regular widespread bed forms that are characterized by vertical and transversal scales which are comparable with the stream depth and width, respectively. Although well-established linear and weakly nonlinear stability analysis have already been performed, no non modal analysis has been proposed yet. We here demonstrate the remarkable non normality of the operator that governs bar dynamics in large regions of the parameter space in fair agreement with our tests in flume experiments. This entails the occurrence of dramatic transient growths in the evolution of bed perturbations. Such algebraic growths suggest a novel explanation, through a purely linear process, of the progressive increase in the dominant bar wavelength that is observed in flume experiments and real rivers during bar inception. The second part of this thesis deals with river antidunes. A supercritical free-surface turbulent stream flowing over an erodible bottom can generate a characteristic pattern of upstream migrating bedforms known as antidunes. This morphological instability, which is quite common in fluvial environments, has attracted speculative and applicative interests, and has always been modelled in 2D or 3D mathematical frameworks. However, in this work we demonstrate that antidune instability can be described by means of a suitable one-dimensional model that couples the Dressler equations to a mechanistic model of the sediment particle deposition/entrainment. The results of the linear stability analysis match the experimental data very well, both for the instability region and the dominant wavelength. The analytical tractability of the 1D modeling allows us (1) to elucidate the key physical processes which drive antidune instability, (2) to show the secondary role played by sediment inertia, (3) to obtain the dispersion relation in explicit form, and (4) to demonstrate the absolute nature of antidune instability.