Conditions for extreme wave runup on a vertical barrier by nonlinear dispersion

The growth of the largest wave in the group is seen to reflect the asymptotic time
scaling provided by nonlinear modulation theory rather closely, even in the case
of fully nonlinear evolution and moderately slow modulations. In order to address
the effect of such a dynamics on the subsequent wall runup, numerical simulations
of evolving long-wave groups are then carried out in a computational wave tank
delimited by vertical walls. Conditions for optimal runup efficiency are sought with
respect to the main physical parameters characterizing the incident waves, namely
the wavelength, the length of the propagation path and the initial amplitude. Extreme
runup is found to be strongly correlated to the ratio between the available propagation
time and the shallow-water nonlinear time scale. The problem is studied in the twofold
mathematical framework of the fully nonlinear free-surface Euler equations and the
strongly nonlinear Serre–Green–Naghdi model. The performance of the reduced model
in providing accurate long-time predictions can therefore be assessed.

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