A fully dispersive weakly nonlinear model for water waves

A fully dispersive weakly nonlinear water wave model is developed via a new approach named the multiterm-coupling technique, in which the velocity field is represented by a few vertical-dependence functions having different wave-numbers. This expression of velocity, which is approximately irrotational for variable depth, is used to satisfy the continuity and momentum equations. The Galerkin method is invoked to obtain a solvable set of coupled equations for the horizontal velocity components and shown to provide an optimum combination of the prescribed depth-dependence functions to represent a random wave-field with diversely varying wave-numbers.