Extreme coastal responses using focused wave groups: Overtopping and horizontal forces exerted on an inclined seawall

For a given focus location and linear focused wave amplitude, variations in phase lead to an order-of-magnitude change in the group overtopping volume. Substantial increases in overtopping volume owing to the use of linear wavemaker theory (compared to second order theory) are also observed. These observations have implications for phase-independent empirical relationships derived using linear paddle signals in physical experiments. Examination of the incidence of wave groups parametrically optimised for maximum (and minimum) overtopping volumes indicates that the overtopping volume may be optimised by minimising reflections of pre-overtopping waves within the group, while maximising the amplitude of the first overtopping bore. Numerical predictions of horizontal seawall forces are obtained using fluid impulse derivatives and hydrostatic pressures obtained from the shallow water model. Within the shallow water model framework, hydrodynamic force contributions included in the fluid impulse method are observed to be small relative to the hydrostatic pressure force. The parametric dependence of the horizontal (non-impulsive) forces on the seawall is very similar to that of the overtopping volumes, with clear 'bands' of large values observed as a function of phase and focus location (for a given amplitude). This suggests that the parametric optimisation of focused wave groups is a robust method for the investigation of multiple coastal responses such as overtopping, forces and runup.