ON SHOALING PROPERTY OF A SET OFFOURTH DISPERSIVE BOUSSINESQ MODEL

When Boussinesq model is applied to compute wave transformation from deep water to shallow water, the proper shoaling effect is essentially important for accurately predicting wave evolution. Improper shoaling parameters value results in bad shoaling property, and decreases the applicability of the Boussinesq model. Based on a fourth order dispersive Boussinesq equations proposed by Madsen and Schäffer (1998), theoretical analysis was reinvestigated, and we pointed out that the α₂ and β₂ values in the reference of Madsen and Schäffer was not proper and re-determined their values. Numerical model was established in staggered grids, and a composite fourth order Adams-Bashforth-Moulton scheme was applied to solve time integration and the model was solved by a predictor-corrector-iteration algorithm in finite difference method. Numerical simulations were applied to two typical cases: One was linear wave propagation over a slow-varying depth, and the other was nonlinear wave evolution over a submerged sill. The computed results with present parameter values were compared against the relevant analytical solution and experimental measurements. Both of the agreements are quite good, which validates the theoretical shoaling analysis numerically.