A study on the stability of laminar open-channel flow over a sandy rippled bed

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 modify 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.