FURTHER ENHANCEMENTS OF BOUSSINESQ-TYPE EQUATIONS

On the basis of two recently published new forms of the Boussinesq equations, yet another set of equations is derived. These new equations represent another step forward in the improvement of the linear dispersion and shoaling characteristics. The linearized version of this new set of Boussinesq equations corresponds to a higher order Fade expansion in kh of the Stokes linear dispersion relation for waves on arbitrary depth. The formulation also allows for an optimization of the linear shoaling properties giving excellent results. The linear dispersion and shoaling characteristics of the new equations are acceptable even for wavelengths as small as the water depth.