Abstract
Bed-load transport at unsteady flow is studied. In gravel-bed streams, the direct effect of flow unsteadiness on bed-load motion promotes the transport discharge and brings positive or negative phase shift. Meanwhile, in sand beds with dunes, the relaxation effect suppresses the sediment discharge and causes the phase lag. Particularly in gravel beds, steep hydrograph often appears, and the former effect dominates. The linear analysis reveals that the amplification of bed-load discharge is reversally proportional to the dimensionless time scale of hydrograph, and that it is correlated to the intensity of phase shift. With the increase of the Froude number and the ratio of bed slope to the relative flow depth, the phase shift increases to become positive. The analytical results are qualitatively well consistent with the flume experiments, and they are helpful to obtain semi-empirical predicting formula for unsteady effect of bed-load transport.
