Estimation of Freak Wave Occurrence From Deep to Shallow Water Regions

Nonlinear four-wave interactions amplify wave heights of deep-water generating extreme wave such as a freak wave. However, it is not clear the behavior of generated freak waves in deep-water shoaling to shallow water regions. In this study, a series of physical experiments and numerical simulations with several bathymetry configurations were conducted for unidirectional random waves from deep to shallow water regions. The maximum wave heights increase with an increase in kurtosis by third-order nonlinear interactions in deep water regions. The dependence of the kurtosis on the freak wave occurrence is weakened due to second-order nonlinear interactions associated with wave shoaling on the slope. Moreover, it is possible to understand the behavior of the high-order nonlinearity and the freak wave occurrence in shallow water regions if appropriate correction of the insufficient nonlinearity of more than O(ε^2) to the standard Boussinesq equation are considered analytically.