Modelling the run-up of significant wave groups

An approximate, but computationally exact, model is presented for evaluating the inundation characteristics of significant wave groups which propagate almost orthogonally to the coast on straight beaches. Run-up and depth-integrated velocities are computed on the assumption that a group of non-breaking waves of finite amplitude shoaling in shallow waters can be represented by a group of solitary-type pulses. The superposition of solitary-type pulses is studied by means of a theoretical model developed from that of Brocchini (1998) to explicitly account for beach slope variations. Characteristics of the groups of solitary pulses in shallow waters are defined by first generating a suitable number of sea states on the basis of spectral theory (Wallops spectrum) and, subsequently, by applying the theory of ‘characteristic groups’. The model allows for direct, easy and fast computation of the flow properties of interest in terms of exact solutions. The application of the model is illustrated by computing the run-up properties of ‘typical groups’. The role of the group characteristics and the beach slope on the run-up intensity is also investigated.