NONLINEAR NUMERICAL STUDY OF NON-PERIODIC WAVES ACTING ON A VERTICAL CLIFF

Abstract

In this study, a 2D fully-nonlinear numerical wave tank is developed based on the time-domain higher-order boundary element method. Non-periodic waves acting on a vertical cliff are investigated. The fully nonlinear kinematic and dynamic boundary conditions are satisfied on the instantaneous free surface. The mixed Eulerian-Lagrangian method is adopted to track the transient water particle on the free surface and the fourth order Runge-Kutta method is used to predict the velocity potential and wave elevation on the free surface. Then the acceleration potential technique is adopted to calculate the temporal derivative of the potential on the vertical wall surface, and transient wave loads are obtained by integrating the Bernoulli equation along the wetted wall surface. The obtained nonlinear results are firstly compared with solutions of the Serre-Green-Naghdi (SGN) theory. It is observed that, for the highly nonlinear case of double-incidentwaves, the SGN model which only satisfies the weak dispersion relationship greatly underestimates the maximum wave run-up (MWR). Then, the nonlinear interaction between double-incident-waves and a vertical cliff is further studied. It is found that the linear prediction also underestimates the MWR. The nonlinearity not only leads to an evident increase of the MWR, but also results in a high-frequency oscillation of the free surface. During this process, nonlinear properties of wave loads are similar to those of the wave run-up. Finally, spectral analysis is performed on histories of wave run-up and wave loads. The dominant frequency wave component is found to transfer its energy to higher frequency components, as a typical nonlinear wave-wave interaction phenomenon.