Nonlinear wave transformation over breakwaters of arbitrary slope

Wave shoaling of water waves over mild bottom slopes is well described by linearized theories. However, analytical treatment of nonlinear wave shoaling subject to rapidly varying bottoms has proven to be elusive in the past decades. As the spatial evolution of the exceedance probability of irregular waves is affected second-order effects in steepness, the nonlinear shoaling coefficient throughout a symmetrical breakwater arbitrary slope is investigated through a stochastic framework. By inverting the effect of slope on normalized wave height distribution, it is possible to obtain a closed-form slope dependence of the nonlinear shoaling coefficient compatible with experiments over symmetrical breakwaters.