caa a22 4500 44530264X CHVBK 20180317142602.0 cr unu---uuuuu 170323e20100801xx s 000 0 eng 10.1134/S0001433810040122 doi (NATIONALLICENCE)springer-10.1134/S0001433810040122 Statistical estimates of characteristics of long-wave run-up on a beach [Elektronische Daten] [I. Didenkulova, A. Sergeeva, E. Pelinovsky, S. Gurbatov] A run-up of irregular long sea waves on a beach with a constant slope is studied within the framework of the nonlinear shallow-water theory. This problem was solved earlier for deterministic waves, both periodic and pulse ones, using the approach based on the Legendre transform. Within this approach, it is possible to get an exact solution for the displacement of a moving shoreline in the case of irregular-wave run-up as well. It is used to determine statistical moments of run-up characteristics. It is shown that nonlinearity in a run-up wave does not affect the velocity moments of the shoreline motion but influences the moments of mobile shoreline displacement. In particular, the randomness of a wave field yields an increase in the average water level on the shore and decrease in standard deviation. The asymmetry calculated through the third moment is positive and increases with the amplitude growth. The kurtosis calculated through the fourth moment turns out to be positive at small amplitudes and negative at large ones. All this points to the advantage of the wave run-up on the shore as compared to a backwash at least for small-amplitude waves, even if an incident wave is a Gaussian stationary process with a zero mean. The probability of wave breaking during run-up and the applicability limits for the derived equations are discussed. Pleiades Publishing, Ltd., 2010 wave run-up on the shore nationallicence nonlinear shallow water theory nationallicence random wave field nationallicence Didenkulova I. Institute of Applied Physics, Russian Academy of Sciences, ul. Ul'yanova 46, 603950, Nizhny Novgorod, Russia aut Sergeeva A. Institute of Applied Physics, Russian Academy of Sciences, ul. Ul'yanova 46, 603950, Nizhny Novgorod, Russia aut Pelinovsky E. Institute of Applied Physics, Russian Academy of Sciences, ul. Ul'yanova 46, 603950, Nizhny Novgorod, Russia aut Gurbatov S. Nizhny Novgorod State University, pr. Gagarina 23, 603950, Nizhny Novgorod, Russia aut Izvestiya, Atmospheric and Oceanic Physics SP MAIK Nauka/Interperiodica 46/4(2010-08-01), 530-532 0001-4338 46:4<530 2010 46 11485 https://doi.org/10.1134/S0001433810040122 text/html Onlinezugriff via DOI 1 brief-communication jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0001433810040122 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Didenkulova I. Institute of Applied Physics, Russian Academy of Sciences, ul. Ul'yanova 46, 603950, Nizhny Novgorod, Russia aut NATIONALLICENCE 700 1- Sergeeva A. Institute of Applied Physics, Russian Academy of Sciences, ul. Ul'yanova 46, 603950, Nizhny Novgorod, Russia aut NATIONALLICENCE 700 1- Pelinovsky E. Institute of Applied Physics, Russian Academy of Sciences, ul. Ul'yanova 46, 603950, Nizhny Novgorod, Russia aut NATIONALLICENCE 700 1- Gurbatov S. Nizhny Novgorod State University, pr. Gagarina 23, 603950, Nizhny Novgorod, Russia aut NATIONALLICENCE 773 0- Izvestiya, Atmospheric and Oceanic Physics SP MAIK Nauka/Interperiodica 46/4(2010-08-01), 530-532 0001-4338 46:4<530 2010 46 11485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer