Optimized Dispersion Characteristics of the Boussinesq Wave Equations

In this paper a new set of Boussinesq wave equations with improved linear dispersion properties is proposed for extending its application to deeper water without having its mathematical form changed. The improvements are due to the combination of a generalized set of Boussinesq wave equations expressed in terms of any velocity, with additional dispersive terms obtained by invoking the linear shallow water equations supplemented by calibration coeecients. The shoaling behavior, particularly important in regions with variable bathymetry, was also accounted for. The resulting equations improve substantially the phase celerity for linear waves in water depths beyond the former formulations. Allowing a 5% phase celerity error the new formulation can be applied up to depth to wavelength ratios of about 1.5. One and two dimensional numerical model simulations of periodic waves travelling into deep water, show the eeectiveness of the proposed equations.