Aftereffect of high-order nonlinearity on extreme wave occurrence from deep to intermediate water

Abstract

Nonlinear four-wave interactions amplify wave heights of deep-water generating extreme wave such as a freak wave and they have become an important topic in engineering and science. However, it is not clear the behavior of extreme waves in deep-water shoaling toward shallow water; the transient behavior of high-order nonlinearity on the slope and its effect on the wave pressure acting on the breakwater. In this study, a series of experiments with several bathymetry configurations from deep to shallow water were conducted for unidirectional random waves. The dependence of the kurtosis on the extreme wave occurrence weakens if dimensionless water depth kh is shallower than 1.363, but the amplified extreme wave still remains until the surf zone. The aftereffects of the deep-water third-order nonlinearity in greater water depth give remarkable influences on random wave height distribution on the slope. Additionally, from the point of view of the design for breakwaters, it is possible to evaluate the uncertainty of wave pressures with the deviation from the Rayleigh theory through the extreme wave occurrence depending on the kurtosis changing.