# Nonlinear integrable equation-based generation of random waves in large-scale basins and flumes

# Nonlinear integrable equation-based generation of random waves in large-scale basins and flumes

Generation of prescribed, scaled physical time series of large-amplitude (including rogue) waves, as measured at particular ocean sites, are often needed in large-scale wave basin (LSWB) experiments to replicate extreme wave impact loads on offshore structures. Current state-of-the-practice models for wave generation in commercial and academic LSWBs worldwide are limited mostly to linear and second-order-term removal types. However, for large-amplitude wave generation, nonlinear models such as nonlinear Schrodinger (NLS) for deep water, Korteweg-de Vries (KdV) for shallow water, and their associated higher-order equations are deemed more accurate for large-amplitude wave simulations. In this study, some analytical and numerical tools we have developed for wave propagation analysis using the periodic and quasi-periodic inverse scattering transform (a.k.a. finite gap) theory based on the NLS and KdV equations propagation, and a nonlinear wavemaker theory (NWMT) based on NLS for wave generation in deep water are presented. The periodic inverse scattering transform allows the notion of a nonlinear spectrum to be defined precisely in the spirit of the linear spectrum of a Zakharov-Shabat operator (for NLS) or Schrodinger operator (for KdV) which can be computed from the Monodromy matrix via the Floquet discriminant that is fundamental to our analysis. The corresponding wave phases can also be determined from the Monodromy matrix by analyzing off diagonal elements. In other words, the IST is a nonlinear Fourier transform representation of periodic solution. Numerical results based on these models will be presented and compared with experimental data for validation. Representative LSWBs at the Oregon State University Hinsdale Wave Research Laboratory will be used as reference for physical wave profile simulations and experimental results discussions.