The free long-wave generation by short-wave groups over a sloping bottom is studied both experimentally and theoretically by various authors showing important results concerning the modelling of energy transfer from the short waves to subharmonics. In the present work, the coupled-mode model developed by Athanassoulis & Belibassakis (1999) for the propagation of water waves over variable bathymetry regions, as generalized to include dissipation due to bottom friction and breaking effects, is applied to calculate the spatial evolution of short-wave groups propagating over a shoaling area, characterized by general bottom topography. Following Scha¨ffer (1993), the present model is appropriately modified in the surf zone in order to destroy the short-wave modulation, keeping the wave height decay in proportion to the local water-depth, and is then used to calculate radiation stresses associated with shoaling and breaking of short-wave groups in the area of general bathymetry and in the surf zone. Subsequently, the system of long wave equations, corresponding to zero (set-down/set-up) and first few harmonics, forced by the radiation stresses, is numerically solved. Results are presented showing that the present model provides reasonable predictions, supporting the study of infragravity waves induced by shortwave groups and their effects on harbors and mooring systems of large vessel operating in nearshore/coastal regions.

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