Transition from migrating alternate bars to steady central bars in channels with variable width

We study the development process of free bars in straight cohesionless channels subject to periodic width changes. The problem is investigated both theoretically and experimentally. We first consider the steady flow in a channel with low amplitude periodic variations of the width. We than perform a linear stability analysis of the latter flow. The main result is a linear dispersion relationship which allows one to determine the correction to the growth rate and migration speed of free bars due to width variations. Theoretical results suggest that width variations may inhibit the development of free bars and trigger the transition from migrating to steady bars. The damping effect increases for increasing values of Shields parameter; it also depends on the wavelength of width variations. Theoretical findings agree almost qualitatively with experimental observations performed in a laboratory flume.