Didenkulova I.I., Sergeeva A.V., Pelinovsky E.N., Gurbatov S.N.
The run-up of irregular long sea waves on a beach of a constant slope is studied in the framework of nonlinear shallow water theory. It is shown that the problem nonlinearity does not influence on statistical moments of the velocity of the moving shoreline, but affects statistical moments of the displacement. In particular, for weak-amplitude waves it is demonstrated that the wave run-up process has a longer duration as compared to the duration of the wave run-down process, even if the incident wave field represents Gaussian stationary process with a zero mean. The probability of wave breaking during the process of wave run-up is calculated and conditions of the model validity are discussed.
