Analyses on grouped wind waves and their associated long waves propagating over composite bottom slopes

In a train of irregular wind waves, high and low waves alternately appear in groups. The existence of the wave groups will induce secondary waves with a period corresponding to that of the groups. The typical period of the long waves observed in a field is around 100s. The long waves are sometimes called “infragravity waves”. During a storm, beach erosion occurs rapidly with sand transport from the foreshore beach to the offshore. Formerly, wind waves were considered to be the main external forces of beach erosion. Even under stormy wind wave conditions, however, the after breaking wave heights in the inner surf zone are limited by the water depth. Therefore, it is difficult to attribute the abrupt beach erosion solely to the wind waves. In contrast, infragravity waves do not break in the surf zone and reach their maximum height at the shoreline. Several field studies have reported that the infragravity waves induced by grouped wind waves play a significant role on the beach erosion. Symonds et al. [1982] proposed a model to explain the generation mechanisms of infragravity waves by temporal breakpoint variance. The breakpoint varies over the period of the grouped waves because higher waves in the group break further offshore than lower waves do. Thus, the time-varying breakpoint is considered to act as a wave maker of the infragravity waves. This study aims to extend the Symonds’ model to the more realistic beach morphology as the bar type beach, and investigates the coupling field of grouped wind waves and their associated infragravity waves, analytically and numerically. Comparisons between the numerical and analytical results are made and the advantage of each method is discussed.