A Study on the Origin of Step-Pool Formation in A Mountain Stream Considering the Water Surface Waves.

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Experiments of ribs and step & pools formation using a laboratory flume with sand-gravel bed, and theoretical analysis for the origins were conducted. They resulted in the followings :(1) In the supercritical flow condition, ribs were formed on the bed, which had a 2-dimensional transversal shape, with active sediment transport and with stagnation of the maximum size stones on the crests.(2) With the trigger of rib formation, 3-dimensional diagonal waves were generated on the water surface.(3) When the resonant condition between water surface wave and rib arose, the water surface waves stood with large amplitudes and deformed the bed waves into 3-dimensional undulations very rapidly.(4) However, the resonant state was not continued so long time ; both the water waves and bed waves ceased to exist with short duration. Only when the water supply was stopped during the occurrence of resonant state, step & pools were found on the bed.(5) Partial occurrence of step & pool system were caused … More by the beat phenomenon between water surface waves and bed waves, which was yielded with different but close wave lengths of them.(6) Multi modal step & pool systems could be found in the channel ; they arose with corresponding to the transverse mode of diagonal water surface waves.Linear stability analysis for the movable boundary, using the plane 2-dimensional momentum equations with non-hydrostatic pressure distribution, revealed the followings :(1) The theoretical step & pool wave length to give the maximum growth rate agrees with the experimental step & pool wave lengths well.(2) Extent of unstable wave number with which step & pools grow up is very narrow, and hence it causes the rapid failure of the step & pools.(3) It can be understood from the analysis that step & pools are 3-dimensional anti-dunes which are formed by the resonant effect of diagonal water surface waves.(4) Concerning with ribs, the unstable wave number domain corresponding to the experimental one is rather difficult to be derived theoretically. Improvement of the theory is needed to apply it to the design of artificial ribs and step & pools. Less