A shallow-water theory of river bedforms in supercritical conditions

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.