Energy balance, wave shoaling and group celerity in Boussinesq-type wave propagation models

This work focuses on the analysis of the linear shoaling performance of low order Boussinesq-type equations. Departing from the equation of the energy balance, a new velocity, vg, is obtained so that Aη2vg is constant in space, being Aη the wave height amplitude. The results are valid for a wide variety of low order Boussinesq-type equations. The new obtained velocity vg, which is in general different to the group celerity cg≡∂ω/∂k, allows a simple and analytical evaluation of the errors in linear shoaling, avoiding the numerical integration of the errors in the linear shoaling gradient. The general results are particularized for well known sets of Boussinesq-type equations.