Beyond Boussinesq-type equations: Semi-integrated models for coastal dynamics.

A novel approach for the description of both wave propagation and flow circulation in the nearshore zone has been defined. This is based on an integro-differential system which, at the leading-order, coincides with classical depth-averaged models (e.g., Boussinesq-type models) and, in addition, describes flow deviations from the depth-averaged values. Thanks to this feature, the proposed system enables exact calculation of the linear dispersion relation, of the linear shoaling coefficient, and of second-order nonlinear solutions for monochromatic waves. A simplified version of the original system has also been proposed. This latter model is exact up to the first order and predicts a linear shoaling coefficient which is comparable with the most advanced, fully nonlinear Boussinesq-type models. The general approach, which can be exploited to obtain a family of models, has clear computational advantages over those which solve the flow over the vertical and improves the flow description accuracy of typical depth-averaged models.