Modelling of the spatial evolution of extreme laboratory wave Heights with the nonlinear Schrödinger and Dysthe equations

Abstract

The spatial evolution of nonlinear wave groups with the same initial Gaussian envelope are theoretically studied under different kind of governing equations, confirming that the higher order nonlinear Schrödinger equation formulation of Dysthe is capable of representing the asymmetric features of propagating wave packets which have narrow spectral bandwidth in deep water. Moreover, laboratory experiments run in an offshore wave basin are systematically compared with a large set of numerical simulations, respectively performed by using the third-order and fourth-order nonlinear wave models, mainly focusing on the aspects of higher order statistical moments such as the coefficients of skewness and kurtosis of the surface elevation, and the exceedance distributions of wave heights in different random sea states. The modulational instability, resulting from a quasi-resonant four wave interaction in the unidirectional sea state, can be indicated by the coefficient of kurtosis, which has shown an appreciable correlation with the abnormal wave density from a statistical point of view. Compared with Dysthe simulation, the NLS model presents a more intensive energy focusing, particularly at the intermediate stage of evolution process in the presence of strong nonlinearity.