A model of wave propagation over a sloping bottom

The propagation of water waves over a sloping beach is known as subject of considerable practical interest. A number of theoretical approaches yielded to exact or approximate solutions of the governing equations under more or less simplified circumstances (Miche (1945), Stoker (1947), ...). Most of these solutions are so complicated and are useless in practice. In this work, te author developed a model which is able to reproduce the main features of the propagation, from these theoretical as well as from some observational results. The work is concerned with the general case of arbitrary values of the bottom slope and the wave incidence angle with respect to the coastline. At first, the bottom is taken as impermeable. Then, an extension to the permeable case is made using Darcy´s law and appropriate conditions at the sea-bottom interface. The author´s work uses the variational technique combined with appropriate forms of the velocity potential to reduce the problem to an ordinary differential equation with respect to the distance to the coast line. Recently, Gagoshidze (1990) developed a model using the Galerkin technique. He found asymptotic solutions for waves at very large distances and at very short distances from the shore