Statistical and Nonlinear Dynamics of Rogue Waves in Varying Bathymetric Environments

Investigating the transformation of ocean surface waves from intermediate to shallow water is essential for predicting extreme coastal events such as rogue waves. In this study, controlled wave-flume experiments employing dispersive focusing were conducted to generate breaking waves with varying spectral bandwidths and nonlinearities. Two bathymetric configurations were examined: a single-sloped profile (Bathy_1) and a compound profile with a steep slope followed by a flat bottom (Bathy_2). The nonlinear dynamics were assessed using wavelet-based bicoherence, whereas the non-Gaussian behavior of rogue waves was investigated in both bathymetric configurations through statistical parameters derived from the time series. In Bathy_2, autobicoherence revealed stronger nonlinear interactions over the steep slope. Kurtosis increased during wave focusing in both bathymetries, while skewness diverged: it decreased and shifted negative in Bathy_2 but increased in Bathy_1. After breaking, both metrics returned to initial levels. Probability distributions in both cases deviated from the Rayleigh model, with the largest discrepancies at the slope end. The compound profile (Bathy_2) showed a higher probability of extreme wave heights. These findings advance understanding of wave evolution by linking bathymetric variability to rogue wave generation and statistical behavior. They highlight the need to incorporate non-Gaussian dynamics and bathymetric effects into predictive frameworks for coastal hazards. Ultimately, the results provide a scientific basis for improving the reliability of coastal engineering design, early warning systems, and risk mitigation strategies in regions vulnerable to extreme wave events.