Modeling the spatial evolutions of nonlinear unidirectional surface gravity waves with fully nonlinear numerical method

Statistical properties of mechanically generated unidirectional nonlinear wave series are simulated with the fully nonlinear Chalikov-Sheinin model, which is based on a non-stationary conformal surface-following coordinate transformation that reduces the principal equations of potential waves into two simple evolutionary equations for the surface elevation and the velocity potential on the surface. Meanwhile, the numerical simulations performed by the temporal version of modified nonlinear Schrödinger equation (MNLS) are also compared with the laboratory experiments in this study. As a result, except for the wave height distribution, Chalikov-Sheinin or simply called CS model performs a little better in simulating the observed statistics than MNLS equation, particularly in the aspects of fourth-order normalized cumulants and the intermediate probability of wave crest and trough exceedance distributions in the presence of strong nonlinearity.