Articles | Volume 18, issue 6
Nonlin. Processes Geophys., 18, 967–975, 2011

Special issue: Nonlinear waves in the ocean

Nonlin. Processes Geophys., 18, 967–975, 2011

Research article 14 Dec 2011

Research article | 14 Dec 2011

Influence of the nonlinearity on statistical characteristics of long wave runup

P. Denissenko1, I. Didenkulova2,3, E. Pelinovsky4, and J. Pearson1 P. Denissenko et al.
  • 1School of Engineering, University of Warwick, Coventry, CV4 7AL, UK
  • 2Laboratory of Wave Engineering, Institute of Cybernetics, Akadeemia tee 21, 12618 Tallinn, Estonia
  • 3Nizhny Novgorod State Technical University, Minin str. 24, 603950, Nizhny Novgorod, Russia
  • 4Institute of Applied Physics, Uljanov str. 46, 603950 Nizhny Novgorod, Russia

Abstract. Runup of long irregular waves on a plane beach is studied experimentally in the water flume at the University of Warwick. Statistics of wave runup (displacement and velocity of the moving shoreline and their extreme values) is analyzed for the incident wave field with the narrow band spectrum for different amplitudes of incident waves (different values of the breaking parameter Brσ). It is shown experimentally that the distribution of the shoreline velocity does not depend on Brσ and coincides with the distribution of the vertical velocity in the incident wave field as it is predicted in the statistical theory of nonlinear long wave runup. Statistics of runup amplitudes shows the same behavior as that of the incident wave amplitudes. However, the distribution of the wave runup on a beach differs from the statistics of the incident wave elevation. The mean sea level at the coast rises with an increase in Brσ causing wave set-up on a beach, which agrees with the theoretical predictions. At the same time values of skewness and kurtosis for wave runup are similar to those for the incident wave field and they might be used for the forecast of sea floods at the coast.