Abstract
Shoaling surface gravity waves induce rogue wave formation, but are reduced to water waves passing over a step. We show that non-equilibrium physics allows finite slopes to be considered in this problem. A spatially varying energy density describes the dependence of the rogue wave amplification as a function of the slope steepness. Increasing the slope increases the amplification of rogue wave probability, until this amplification saturates at steep slopes. In contrast, the increase of the down slope of a subsequent de-shoal zone leads to a monotonic decrease in the rogue wave probability. In view of the central role played by the excess kurtosis in estimating rare event probabilities, we find an effective theory for the excess kurtosis evolving over a shoal.
