In this study, a theoretical solution of the nonlinear interaction of two free wave trains crossing infinite water depth has been expanded to the 3rd-order, employing the perturbation method. The water surface elevation and particle velocities have been Investigated. Laboratory experiments were also carried out to examine the validity of the proposed theory. The proposed theory is shown to evaluate well the experimental results The skewness of the water surface elevation and particle velocities of the crossing waves are fairly affected by each wavelength of two wave trams and the crossing angle.
The sea waves in nature are generally complex in form and random, and they are composed of many component waves with different heights, periods and wave directions, which are mutually interacted. The strong interaction of nonlinear waves, however, gives rise to new hydraulic characters which are difficult to be expected in the linear interaction. The freak waves have been pointed out to occur under this nonlinear interaction. Therefore, it is important to investigate the nonlinear interaction of waves such as the incident and reflected waves, the wind waves themselves, and the swell and wind waves. In recent years much interest has been paid to the nonlinear interaction of waves with the increasing utilization of coastal and ocean region; The nonlinear interaction solution of the crossing incident and reflected waves with the same wave periods in front of rigid wall has been expanded to the 3rd-order, over a few decades, by Fuchs(1952} and Hsu, et. al.(1979). Tick(1959) first dealt with the interaction of multiple component waves, and he discussed the nonlinear spectrum of deep water waves. Hamada(1965) and Hwung and Tsai(1982) theoretically investigated the secondary interaction of two component waves in finite water depth. Phillips(1960) and Longuet-Higgins(1962} discussed the nonlinear interactions of two free waves with different wave periods in deep water depth and found that the resonant interaction occur in the 3rd-order term.