The bed of a river often features some kinds of bedform, such as sand ripples, dunes, and so on. Even if the bed is smooth initially, disturbances arising from the bed or other external sources will cause the laminar flow in an open channel to become unstable as soon as the flow develops, thereby leading to the formation of sand ripples on the bed. In return, the formation of the sand ripples will modfy the instability path of the laminar flow passing over them. The wavy character of the bed will induce further instability of the flow, which is essentially different from that on a smooth bed: the neutral curve will move forward and the critical Reynolds number will decrease. The flow is unstable in response to a wider range of the disturbance wave number, or the laminar flow instability can happen more easily. The propagation speed of the sand ripples also affects the flow instability, since the stability of open channel flow over a movable bed is fundamentally different from that on a rigid bed. These instability effects are discussed in detail in this paper.
Bed forms of various kinds that evolve naturally on the bottom of sandy coasts and rivers are a result of the kinematics of bed load transport. Based on the group motion of particles in the bed load within the bottom layer, a study on the nonlinear dy- namics of bed load transport is presented in this paper. It is found that some development stages, such as the initiation, the equilibrium sediment transport, and the transition from a smooth bed to sand dunes, can be accounted for by different states in the nonlinear sys- tem of the bed load transport. It is verified by comparison with experimental data reported by Laboratoire Nationae D’Hydraulique, Chatou, France, that the evolution from a smooth bed to sand dunes is determined by mutation in the bed load transport. This paper pre- sents results that may offer theoretical explanations to the experimental observations. It is also an attempt to apply the state-of-the-art nonlinear science to the classical sediment transport mechanics.
