Application Of Higher Order Boussinesq Equation Simulation Of Complex Terrain Of Wave Propagation And Deformation

The applicability of six different wave-propagation models in nonlinear dispersive wave fields has been investigated. The three of them are the higher order Boussinesq equations derived by Zou (1999) and the others are the classical Boussinesq equations, the equations which is obtained by deducting the G term from the two-parameter equations and the equations which is abtained by deducting the terms that contain B1and B2 from the two-parameter equations.A Predictor-Corrector finite difference scheme was employed to solve the equations numerically. Physical experiments were conducted 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 were employed in the experiment and their effects on the wave propagation were investigated. The comparisons of the numerical results with test data were made and the applicability of the six models was discussed.As expected, the higher order Boussinesq equations (the two-parameter equations, three-parameter equations and equations of (2-33)and (2-34)) agree better with the measurements than the classical Boussinesq equations. The numerical results show that the good results can also be obtained for the steep slope case although the mild slope assumption was employed in derivation of the higher order terms in the two-parameter Boussinesq equations and the three-parameter Boussinesq equations. The numerical results of the equations (2-33) and (2-34) also agree well with the test data, which indicates the high accuracy of the numerical model. In the last part of this paper, the effects of the high-order nonlinear and dispersive terms contained in the two-parameter Boussinesq equations are discussed.The results of comparisons show the numerical models of higher order Boussinesq equations (the two-parameter equations, three-parameter equations and equations of (2-33) and (2-34)) set up in this paper can give good results in predicting waves properties.