Abstract
Existing dispersive wave equations, such as Boussinesq equation, are derived with an asymptotic expansion around the long wave limit, and hence their applicability is restricted to the shallow water. To break through the restriction, in the present study, fully-dispersive wave equations have been developed through a formulation based on the Galerkin method. The newly derived equations can simulate irregular wave fields with wide spectrum range extending over shallow to deep water region. The validity of the wave equations has been confirmed through the comparison of their numerical solutions with the theories both for Cauchy-Poisson and irregular waves. The discussions are given also about the fundamental characteristics, such as the dispersivity, of the new wave equations.
