THE PROPAGATION OF SURFACE-WAVES IN FLOW DOWN AN OSCILLATING INCLINEDPLANE

The propagation of surface waves is investigated theoretically and exp erimentally for the case of a single layer of viscous liquid flowing d own an inclined plane, where the plane is oscillating in the flow dire ction. This work focuses on the linearized wavemaker problem, where th e oscillations create waves which are small perturbations from the und isturbed flow. Downstream from the entrance region to the incline wher e the fluid is introduced, the undisturbed interface is parallel to th e incline surface, and theory predicts that oscillations do not intera ct with waves that travel along the free surface. These waves grow as if there were no oscillation at all, and their propagation is governed by a dispersion relation between frequency, wavelength, and wave grow th for single layer flow down a nonoscillating inclined plane. The ent rance region to the incline is therefore responsible for exciting the various wave frequencies which are observed down the incline, as well as the initial amplitude of these waves. Experiments performed verify that waves propagate as predicted. Theory indicates that these conclus ions are valid when the oscillations are perpendicular to the incline, as well as for the case of multiple stacked layers.