On the analysis of 2D nonlinear gravity waves with a fully nonlinear numerical model

Abstract

A fully nonlinear numerical method, developed on the basis of Euler equations, is used to study the dynamics of nonlinear gravity waves, mainly in the aspects of the propagation of Stokes wave with disturbed sidebands, the evolution of one wave packet and the interaction of two wave groups. These cases have previously been studied with the higher order spectral method, which will be an approximately fully nonlinear scheme if the order of nonlinearity is not large enough, while the present method in the case of the 2D model has an integration scheme that is exact to the computer precision. As expected, in most cases the results are consistent between these two numerical models and it is confirmed again that this fully nonlinear numerical model is also capable of maintaining a high accuracy and good convergence, particularly in the long-term evolutionary process.