A new expression for the set-up for random wind generated waves

In this study a new analytical solution for estimating the set-up (defined as the time-averaged water-level run-up at the shoreline) for irregular random wind-generated waves is proposed. A closed-form expression for the definition of set-up is derived for progressive random waves using the sea states theory. The classical Longuet-Higgins approach, proposed in 1963, for calculating the set-up for periodic waves is extended to the case of irregular sea waves. Then, numerical results are provided. The solution is validated by processing buoy data from two different locations: in the Mediterranean Sea, off the western coast of Alghero, Sardinia (Italy), and in the Pacific Ocean, off the coast of Santa Barbara, California (USA). The estimation results for the set-up for random waves obtained using the proposed solution are compared with those obtained using a simplified model of monochromatic periodic waves. The proposed solution is found to provide more accurate results and predictions.