Generation of two-dimensional steep water waves on finite depth with and without wind

This paper reports on a series of numerical simulations designed to investigate the action of wind on steep waves and breaking waves generated through the mechanism of dispersive focusing on finite depth. The dynamics of the wave packet propagating without wind at the free surface are compared to the dynamics of the packet propagating in the presence of wind. Wind is introduced in the numerical wave tank by means of a pressure term, corresponding to the modified Jeffreys' sheltering mechanism. The wind blowing over a strongly modulated wave group due to the dispersive focusing of an initial long wave packet increases the duration and maximal amplitude of the steep wave event. These results are coherent with those obtained within the framework of deep water. However, steep wave events are less unstable to wind perturbation in shallow water than in deep water.Furthermore, a comparison between experimental and numerical wave breaking is presented in the absence of wind. The numerical simulations show that the wind speeds up the wave breaking and amplifies slightly the wave height.The wall pressure during the runup of the steep wave event on a vertical wall is also investigated and a comparison between experimental and numerical results is provided.