A third-order Boussinesq model applied to nonlinear evolution of shallow-water waves
This paper is devoted to the derivation of new third-order Boussinesq shallow water equations. These equations describe the evolution of a weakly nonlinear and dispersive wavetrain over a slowly varying bottom topography. It is shown that the new equations possess better linear dispersion characteristics. The new equations are used to study the evolution of periodic waves and the generation of higher harmonics in water of constant depth. Special attention is given to numerical computational results and to comparison between the conventional and new Boussinesq models. It is shown that the new third-order Boussinesq model enhances the spatial aperiodicity and skewness of the wave envelopes, shortens the beat distance, and thus more energy is transferred from lower harmonics to higher harmonics. The results are compared with experimental data as well as with previous results based on the conventional Boussinesq equation. The results of this paper seem to be more satisfactory than those obtained by previous authors.
nonlinear evolution of shallow water waves
third-order Boussinesq shallow water equations
scientific article; zbMATH DE number 1508362