A second order analytical solution of focused wave group interacting with a vertical wall

The interaction of focused wave groups with a vertical wall is investigated based on the second order potential theory. The NewWave theory, which represents the most probable surface elevation under a large crest, is adopted. The analytical solutions of the surface elevation, velocity potential and wave force exerted on the vertical wall are derived, up to the second order. Then, a parametric study is made on the interaction between nonlinear focused wave groups and a vertical wall by considering the effects of angles of incidence, wave steepness, focal positions, water depth, frequency bandwidth and the peak lifting factor. Results show that the wave force on the vertical wall for obliquely-incident wave groups is larger than that for normally-incident waves. The normalized peak crest of wave forces reduces with the increase of wave steepness. With the increase of the distance of focal positions from the vertical wall, the peak crest of surface elevation, although fluctuates, decreases gradually. Both the normalized peak crest and adjacent crest and trough of wave forces become larger for shallower water depth. For focused wave groups reflected by a vertical wall, the frequency bandwidth has little effects on the peak crest of wave elevation or forces, but the adjacent crest and trough become smaller for larger frequency bandwidth. There is no significant change of the peak crest and adjacent trough of surface elevation and wave forces for variation of the peak lifting factor. However, the adjacent crest increases with the increase of the peak lifting factor.