Irregular Wave Setup and Run‐up on Beaches

Abstract

The one‐dimensional equations of mass, momentum, and energy are derived from the two‐dimensional continuity and Reynolds equations in order to elucidate the approximations involved in these one‐dimensional equations, which have been used previously to predict normally incident wave motions on coastal structures and beaches. The numerical model based on these equations is compared qualitatively with the wave setup and swash statistics on a moderately steep beach with a nearshore bar. The numerical model is shown to predict the irregular wave transformation and swash oscillation on the barred beach, at least qualitatively. The computed setup and swash heights are found to follow the lower bound of scattered data points partly because of the neglect of the longshore variability on the natural beach and low‐frequency components in the specified incident wave train. A more quantitative comparison is also made with the spectrum of the shoreline oscillation measured on a 1:20 plane beach, for which the corresponding wave spectrum was given. The numerical model is shown to predict the dominant low‐frequency components of the measured spectrum fairly well.