Steady solutions of high-level Irrotational Green-Naghdi equations for strongly nonlinear periodic waves

The Irrotational Green-Naghdi (IGN) equations are categorized into different levels. The low-level IGN equations can be used in the propagation of weakly dispersive and strongly nonlinear waves. On the other hand, high-level IGN equations can deal with strongly dispersive and strongly nonlinear waves. We focus here on the simulations of the steady solutions of nonlinear periodic waves by a low-level IGN (IGN-2) equations and high-level IGN (IGN-4 and IGN-8) equations. In numerical tests, results of wave speed, wave profile and velocity distribution are given for finite-depth water waves and for four different wave lengths as well as for large amplitude deep water waves. By comparing the simulation results, high-level equations are shown to be in better agreement with an accurate theory, namely the stream function wave theory.