Run-up of long waves on an inclined plane

Non-linear wave reflection on inclined planes is studied. Analytical expressions which describe the run-up and the back-wash are obtained both for single and periodic waves. The maximum run-up height for a single harmonic wave compare well with observations of solitary waves on relatively steep slopes. A simple breaking criterion for the collapse of a solitary wave during the back-wash is deviced. The criterion is found to agree well with observations. From the form of the water surface during the run-up we have estimated the possible water spill-over into a reservoir. Energy consideration indicate that less than 30 per cent of the wave energy may be available for power production.