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 ve locity field is represented by a few vertical-dependence functions hav ing different wave-numbers. This expression of velocity, which is appr oximately irrotational for variable depth, is used to satisfy the cont inuity and momentum equations. The Galerkin method is invoked to obtai n a solvable set of coupled equations for the horizontal velocity comp onents and shown to provide an optimum combination of the prescribed d epth-dependence functions to represent a random wave-field with divers ely varying wave-numbers. The new wave equations are valid for arbitra ry ratios of depth to wavelength and therefore it is possible to recov er all the well-known linear and weakly nonlinear wave models as speci al cases. Numerical simulations are carried out to demonstrate that a wide spectrum of waves, such as random deep water waves and solitary w aves over constant depth as well as nonlinear random waves over variab le depth, is well reproduced at affordable computational cost.