A wave model based on the boussinesq equations

An alternative method to derive a set of fully nonlinearBoussinesq equations up to the order of O(\mu^2, \varepsilon^3\mu^2) ispresented. The linear dispersion relation and the shoaling gradient of theequations are improved by adding some dispersive terms. The lineardispersion relation of the enhanced equations is the Pad\'e 4,4expansion of the linear Stokes dispersion relation, the accuracy of which isacceptable even when the relative water depth is as large as 1.0. Itsnonlinear property and shoaling gradient are also improved. Thehorizontal one-dimensional equations are solved with a predictor-correctorfinite difference scheme and a fully nonlinear Boussinesq wave model isestablished, which enjoys high computational efficiency and reliability. Thenumerical model is verified by simulating the transformation of wavespropagating over a submerged bar. The numerical results are verified againstthe laboratory experimental data, and their agreement is found to be very good.