Alternating bar instabilities in unsteady channel flows over erodible beds

Channel flows over erodible beds are susceptible to instabilities of the coupled fluid and sediment flow equations. The most dangerous mode usually takes the form of a migrating alternating bar instability propagating in the flow direction. Previous theories have assumed that the underlying flow is steady and here the theory is extended to the unsteady situation. Stability characteristics are calculated for large-amplitude oscillations superimposed on a mean flow. In addition it is found that the basic instability is convective and we address the receptivity problem for bars induced by flow oscillations interacting with spatial variations associated with seepage, channel width variations etc. The effect of unsteadiness in the weakly nonlinear situation is also discussed. A mechanism which allows flow oscillations to interact with migrating bars to produce a sinusoidal structure fixed in space which might be relevant to meander formation is discussed.