Long waves in erodible channels and morphodynamic influence

Like most media, open channel flows propagate information through waves. When the channel boundary is fixed, the vectors of information consist typically of surface gravity waves. In the less straightforward case of channels with cohesionless bed and possibly erodible banks, other types of waves arise from the erodible nature of the boundaries and the ability of the stream to transport sediments. In this paper we restrict our attention to the important case of long waves, which can be described by employing the shallow water approximation for the flow field and a quasi-equilibrium assumption for sediment transport on weakly sloping beds. We focus on a major issue: In which direction is information propagated? This is a problem raised and partially solved by de Vries in the context of one-dimensional morphological modeling as early as 1965. We review some of the available knowledge on this subject, viewed in a more general context where vectors of information can be a variety of waves: purely longitudinal onedimensional sediment waves, two-dimensional waves driven by large-scale bed forms (bars), and plan form waves carrying information related to the planform shape of the channel. Both linear and nonlinear, migrating and stationary waves are considered. It turns out that the role played by the Froude number in determining the direction of one-dimensional perturbations of bed topography is somewhat taken by the aspect ratio of the channel when large-scale two-dimensional bed forms as well as planform waves are considered.