Stability Characteristics Of Laminar Flow On Sand Ripples In Open Channel

Riverbed is not so even, and it is always accompanied by certain forms, such assand ripple, sand dune and so on, which determine the resistance of the riverbed, themovement of the sediment and the structure of the current etc. Even it is on an even bed, flow will become unstable and sand ripples willappear because of the external disturbances soon after the flow begins, which alsochanges the instability trace of the laminar flow on it. The instability of the laminar flow on the sand ripples in the open channel isdiscussed in this paper, which can help us understand the dynamical principles thatthe flow interacts with the riverbed. Floquet Theory is used to analyze the problem and spectral collocation method,Muller method and QR method are adopted to calculate the model that established. Through the theoretic analyzing and the numerical calculating, some importantconclusions are reached:(1)The characteristics of the laminar instability in the open channel has relationshipwith Reynolds number and has nothing to do with Froude number whether it is on theplane bed or on the sand ripples.(2)The bed amplitude has deep effect on the characteristic of the laminar instability(the circular frequency and the growth rate of the disturbance wave) in the openchannel.(3)The bed amplitude (height of sand ripples) contributes a lot to the neutral curve.The boundary disturbance caused by the bed amplitude can make the laminar flowbecome unstable under a rather lower Reynolds number; moreover the neutral curvewill become straight and not so sensitive to the wave number with the increase of thebed amplitude.(4)The bed amplitude make it different in the distribution of the contour of thecircular frequency and the growth rate of the disturbance wave.(5)Reynolds number has effect on the circular frequency and the growth rate whenit is on sand ripples. With the increase of the Reynolds number, the growth rateincreases significantly, and the circular frequency decreases.(6)The propagation frequency of the sand ripples also effects the stability conditionof the laminar flow in open channel. With the increase of the propagation frequency,the disturbance frequency increases first and then decreases, and the growth rateincreases significantly. These conclusions set a foundation on the later theoretical researches on the bedevolution in the lower reach of Yellow River near estuary and the interaction of theriverbed and the current.