Higher Order Boussinesq Equation Numerical Model

In this paper, the applicability of two wave-propagation models in nonlinear dispersive wave fields has been investigated. They are the improved higher-order Boussinesq equation derived by Zou(l 999),and the higher-order Boussinesq equations for the case of strong current derived by Zou(2000). The results of them are compared with other two wave models, which are the higher order Boussinesq equations derived by Zou (1997), the equations for the case of wave propagating over rapidly varying topography Zou(2001),A Predictor-Corrector finite difference scheme is employed to solve the equations numerically. Physical experiments data are analyzed for wave evolutions passing over a submerged shelf under various wave conditions. Three different front slopes (1:10, 1:5 and 1:2) and two different back slopes (1:5,1:2) of the shelf are employed in the experiment and their effects on the wave propagation are investigated. The comparisons of the numerical results with test data are made and the applicability of the four models is discussed.As expected, the higher order Boussinesq equations (the two-parameter equations, six-parameter equations and higher-order Boussinesq equations for rapidly varying topography agree well with the measurements. In many case, six-parameter equations can agree better than the other two equations, which shows it has higher nonlinear and dispersion accuracy. The numerical results show that the good results can also be obtained for the steep slope case although the mild slope assumption is employed in derivation of the higher order terms in the two-parameter Boussinesq equations and the six-parameter Boussinesq equations. The numerical results of the higher-order boussinesq equations for rapidly varying topography show that it have better applicability in the case of longer wave. The result shows that higher-order Boussinesq equations with strong currents can apply well for the wave-currents interactions.The results of comparisons show the numerical models of higher order Boussinesq equations (six-parameter equations and higher-order Boussinesq equations with strong current) set up in this paper can give good results in predicting waves properties.