Effect of shoaling length on rogue wave occurrence (Q6629576)

The paper addresses a significant problem in coastal engineering and hydrodynamics. Specifically, it examines how the length and characteristics of bathymetric shoaling influence the statistical likelihood of rogue wave occurrences in nonlinear wave systems.\N\NThis research investigates the dynamic processes underlying wave evolution over bathymetric gradients, particularly in nonlinear regimes. The authors employ a combination of theoretical modelling and fully nonlinear potential flow (FNPF) numerical simulations to disentangle the effects of shoaling length from other contributing factors like slope magnitude. The study uses a non-homogeneous second-order wave theory to derive explicit analytical approximations for statistical measures such as kurtosis, a key indicator of rogue wave likelihood, and validates these findings through high-fidelity numerical experiments conducted in a wave flume.\N\NKey methods include defining a dimensionless parameter for shoaling length relative to wavelength, enabling a systematic investigation of its role in wave transformation. The simulations focus on cases where slope magnitude is held constant while varying the shoaling length. Numerical models are calibrated to ensure precision in capturing complex wave dynamics, particularly as they transition through regions of non-equilibrium.\N\NThe findings reveal that the shoaling length parameter does not significantly influence the rogue wave probability once the slope length surpasses a critical threshold relative to the peak wavelength. Instead, the slope magnitude emerges as the dominant factor affecting statistical measures of wave nonlinearity, including kurtosis and skewness. This insight challenges prior assumptions about the role of shoaling abruptness and highlights the necessity of considering slope-induced non-equilibrium dynamics in understanding rogue wave formation.\N\NThis work is significant for advancing theoretical and numerical approaches to wave mechanics and offers critical insights for engineering applications, particularly in designing coastal and offshore structures to mitigate extreme wave impacts. By clarifying the interplay between slope characteristics and wave statistics, this study contributes substantially to the predictive understanding of rogue wave phenomena in coastal environments.