Improved Performance in Boussinesq-Type Equations

In this paper, simple but effective techniques are used to improve the performance of two commonly-used sets of Boussinesq-type equations. The O(μ²) equations of Wei et al.are extended through a redefinition of the reference velocity variable, which allows both linear shoaling and nonlinear properties to be improved significantly. Computational examples of nonlinear shoaling waves demonstrating this improvement are presented. The enhanced equations of Madsen and Schäffer are improved through a comparison with the higher-order Boussinesq equations of Gobbi and Kirby Through the selective cancellation of higher-order terms, equations result that are linearly of O(μ⁴) for a flat bed and for mild slopes in two dimensions. Properties on a flat bed are identical to Madsen and Schäffer, but performance on a sloping bed is significantly improved.