A new Boussinesq-type model for surface water wave propagation

A new Boussinesq-type model for surface water wave propagation in coastal regions is derived. The model is fully nonlinear and accurate to {dollar}O(musp4),{dollar} where {dollar}mu{dollar} is the wave number nondimensionalized by the water depth. As an extension to the second order model proposed by Nwogu (1993), a new dependent variable is defined as a weighted average between the velocity potential at two distinct water depths to force the model to have a (4,4) Pade approximation of the exact linear dispersion relationship. The fourth order polynomial approximation for the velocity potential vertical profile represents a great improvement over existing {dollar}O(musp2){dollar} models, specially over the intermediate to deep water range. Nonlinear effects including generation of super and subharmonics, and amplitude dispersion are investigated. A finite-difference numerical scheme is developed for the 1-dimensional version of the model for the free surface displacement and a velocity-type variable. Several solitary wave solutions are studied and compared with other models, as well as the solution to the full problem. Computations of waves propagating over submerged bars are compared with laboratory measurements and with results of the fully nonlinear {dollar}O(musp2){dollar} Boussinesq model by Wei et al (1995). All computations show that the present model represents a considerable improvement over the {dollar}O(musp2){dollar} model.