FREE-SURFACE PROFILE OF OPEN-CHANNEL FLOW WITH WAVY BOUNDARY

The water-surface profiles over the wavy bed and along the wavy side wall are analytically investigated using a Laplace equation. The nonlinear dynamic and kinematic conditions on the free surface are treated by the perturbation method and analytic solutions are obtained. As a result, the shapes of the crest of the water-surface profile are flatter in length than that of the trough over and along the wavy boundary in subcritical flow. In supercritical flow, the shapes of the crest are more peaked and shorter than that of the trough over and along the wavy boundary. The theoretical result of the water-surface profile of the open-channel flow over the wavy boundary is in good agreement with the experiments. The theoretical result for the flow along the wavy side wall in subcritical flow is also good agreement with experiment, but it in supercritical flow is not.