Wave Reflection and Transmission in Channels of Gradually Varying Depth

Abstract

This report presents the results of a study on the reflection and transmission of water waves in a rectangular channel with transitions of linearly varying depths. Two channel sections of uniform depths are joined by sections of slopes 1:0.58, 1:2.75 and 1:16 in the three sets of experiments. Wave conditions were systematically varied to cover the range of deep-water to shallow-water waves in the deeper approach channel. The pertinent parameters considered for each slope were relative depth (ratio of upstream to downstream depth), ratio of group velocities and wave steepness. Since a comprehensive theory does not exist, the classical small wave amplitude theory for abrupt transitions was employed to correlate the results of the study. Comparisons with other theories developed recently were made where applicable. Some of the important conclusions are: 1. For short and intermediate waves reflection coefficients become generally larger than predicted as the slope of the transition decreases. 2. For short and intermediate waves transmission coefficients generally agree with predictions for group velocity ratios near unity, but tend to lower values for lower ratios of group velocity as the slope of the transition decreases. 3. For short and intermediate waves wave steepness has a relatively small influence on reflection and transmission coefficients. 4. For shallow water waves the reflection coefficients were found independent of relative depth ratios contrary to prediction but decreased markedly with increasing wave steepness for the smallest slope. 5. For shallow water waves the transmission coefficients followed the predicted trend, but became relatively lower for increasing relative depth ratios. Increasing wave steepness had the effect of increasing the transmission coefficients for the smallest slope.