Transient growths of stable modes in riverbed dynamics

Fluvial bars are regular widespread bedforms 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 nonmodal analysis has been proposed yet. We here demonstrate the remarkable nonnormality 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.