A 2DH nonlinear Boussinesq-type wave model of improved dispersion, shoaling, and wave generation characteristics

A modified Boussinesq-type model is derived to account for the propagation of either regular or irregular waves in two horizontal dimensions. An improvement of the dispersion and shoaling characteristics of the model is obtained by optimizing the coefficients of each term in the momentum equation, expanding in this way its applicability in very deep waters and thus overcoming a shortcoming of most models of the same type. The values of the coefficients are obtained by an inverse method in such a way as to satisfy exactly the dispersion relation in terms of both first and second-order analyses matching in parallel the associated shoaling gradient. Furthermore a physically more sound way to approach the evaluation of wave number in irregular wave fields is proposed. A modification of the wave generator boundary condition is also introduced in order to correctly simulate the phase celerity of each input wave component. The modified model is applied to simulate the propagation of breaking and non-breaking, regular and irregular, long and short crested waves in both one and two horizontal dimensions, in a variety of bottom profiles, such as of constant depth, mild slope, and in the presence of submerged obstacles. The simulations are compared with experimental data and analytical results, indicating very good agreement in most cases.