One-dimensional numerical models of higher-order Boussinesq equations with high dispersion accuracy

Nonlinear water wave propagation passing a submerged shelf is studied experimentally and numerically. The applicability of the wave propagation model of higher-order Boussinesq equations derived by Zou (2000, Ocean Engineering, 27, 557~575) is investigated. Physical experiments are conducted; three different front slopes (1:10, 1:5 and 1:2) of the shelf are set-up in the experiment and their effects on the wave propagation are investigated. Comparisons of the numerical results with test data are made and the higher-order Boussinesq equations agree well with the measurements since the dispersion of the model is of high accuracy. The numerical results show that the good results can also be obtained for the steep-slope cases although the mild-slope assumption is employed in the derivation of the higher-order terms in the higher-order Boussinesq equations.