Abstract: Conventional models for wave evolution in coastal zones, cannot account for the influences of irregular slopes and strong nonlinear wave fields in quickly changing seabed topography. This results in fragmented or heuristic estimates that lack smooth transitions and deeper physical understanding. This work presents a stochastic framework for predicting the transformation of extreme waves, including shoaling coefficients, set-down/set-up in the mean water level, and run-up over steep slopes and breakwaters. Building on statistical techniques from extreme waves, we reverse the inhomogeneous exceedance probability curves to obtain an explicit, slope-dependent nonlinear amplification term. This approach integrates second-order steepness effects and partial reflection, validated against large-scale flume experiments over symmetrical breakwaters. Through estimation of the distribution of random phase in limited depths, the system allows straightforward calculation of shifts in the mean sea level, bypassing energy and momentum fluxes, from shoaling-induced set-down to dissipation-driven set-up through non-ergodic spectral analysis and inversion of the second moment integral, ensuring continuity across the entire water depth range without ad hoc breaking criteria. Combining this with mechanical energy conservation, we better understand the run-up growth in breaking waves and the otherwise saturation in non-breaking waves.
Bio: 
Dr. Saulo Mendes obtained his B.Sc. in Physics in Brazil, a M.Sc. in Theoretical Physics at Pontifical Catholic University of Rio de Janeiro (PUC Rio), followed by a Ph.D. in Oceanic Fluid Mechanics at UNC Chapel Hill under the supervision of Prof. Alberto Scotti. He then joined the group of Prof. Kasparian as a research fellow at the Applied Physics Laboratory of the University of Geneva (Switzerland). He was a Lecturer in Mechanical Engineering at Shanghai Jiao Tong University before joining Nanyang Technological University as an Assistant Professor in Civil Engineering.