Modified mild-slope equations for wave propagation

The distributions of velocity potential over the water column for deriving both it the mild-slope equation and the Boussinesq equations have been unif ied. New equations of the Boussinesq type are derived by using the variatio nal principle. The derived non-linear equations approach the Boussinesq equ ations in shallow water. The linear version is essentially the same as the mild-slope equation which is valid over the entire range of water depths. N umerical solutions of the new equations have been compared to experimental data and good agreement has been achieved.