Numerical model simulations of wave propagation and wave run-up on dikes with shallow foreshores

Shallow foreshores considerably affect wave propagation and hence wave run-up on coastal structures. This concerns for instance the evolution of wave height distributions and wave energy spectra between deep water and the toe of coastal structures. Based on numerical model investigations and physical model tests it was concluded that wave run-up and wave overtopping can best be described using wave conditions at the toe of the coastal structures, in particular using the wave period T_m-1,0. With this wave period the effects of arbitrarily-shaped wave energy spectra on wave run-up and wave overtopping can be taken into account. In this paper estimates of wave conditions, including estimates of this wave period T_m-1,0, are obtained using a spectral wave model and a time-domain Boussinesq-type wave model. Especially the applied Boussinesq-type wave model appeared to be appropriate for conditions with severe wave breaking on a shallow foreshore where also a considerable amount of energy is transferred to lower frequencies. Also wave interaction with the dike itself was modelled numerically.