Statistical Estimates of ‎Characteristics of Long Wave Run-up on a Beach ‎

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.

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