Nonlinear wave dynamics in shallow water

This paper presents a set of higher order Boussinesq equations with enhanced dispersion characteristics. For the sake of simplicity the presentation is limited to one-dimensional equations on a horizontal bottom. A Fourier analysis of the equations is performed and it is concluded that the equations incorporate linear dispersion characteristics corresponding to a Pade [4/4] expansion of the exact Stokes relation for linear waves on an arbitrary depth. The equations are solved numerically and compared to measurements of wave transformation over a submerged bar in shallow water. The accuracy is found to be superior compared to what can be obtained by use of classical Boussinesq equations.