In the study, the behavior of a random wave train in the surf zone is investigated. An ideal, original, linear, Gaussian wave train of finite bandwidth propagating from deep water through shoaling region and surf zone onto a straight beach over gently varying seabed of straight parallel contours is allowed to break. The statistical properties examined are mean value, standard deviation and spectrum of breaking waves and mean water level variation.
As a train of random waves propagates shoreward from deep to shallow water through shoaling region and surf zone, it experiences changes in mean water level and wave breaking. While detailed knowledge of the mechanism underlying wave breaking is still lacking, ad hoc wave breaking models have been introduced (see for example, Battjes and Janssen, 1978, Yuan et ai, 1986, Tung and Huang, a, b, c, d, Yang, 1991) for practical applications. In 1991, Yang considered the effects of wave breaking on various statistical properties including the spectrum of a linear, Gaussian, random wave train of narrow bandwidth propagating from deep to shallow water. It was found that wave breaking effectively modifies wave spectrum but spectral shape remains unchanged, contrary to results obtained from laboratory and field investigations. Based on knowledge gained in prior studies (Yuan et ai, 1986, Tung and Huang, 1987 a, b, c, d) it is believed that the afore-mentioned discrepancy will be alleviated if bandwidth of wave train was treated as finite. It is the purpose of this study to examine the effects of wave breaking on the mean value, standard deviation, spectrum and mean water level(set-up, set-down) of a linear, Gaussian wave train of arbitrary bandwidth propagating in water of finite depth with particular attention given to surf zone where active wave breaking takes place and wave spectrum is greatly modified.