Simulation of evolution of gravity wave groups with moderate steepness

•We conduct physical experiments to investigate the evolution of wave groups.•The linear solution of the high-level Green–Naghdi (GN) equations is given.•We check the self-convergence of the GN models by use of GN-3 and GN-4 models.•Good agreement is found between the GN results and experimental data.

The evolution of nonlinear deep-water wave groups in one-horizontal dimension is studied. The strongly nonlinear Green–Naghdi (GN) models are used to simulate this phenomenon. There are different levels of the GN models depending on the different velocity assumption used for the vertical structure of the flow field, such as GN-1, GN-2, and so forth. In this work, we use both the GN-3 and GN-4 models to do the simulations. Calculations are done for three different numbers of waves per group (or packet) as the number of envelope solitons depends on the number of waves per group (N). The numerical results show that the GN-3 model can give the converged GN results for the cases tested here. We conduct a series of physical experiments to investigate the evolution of wave groups. We also use other’s experimental data and present laboratory measurements to compare the data with the predictions of the GN models and show that good agreement is obtained overall.