An undular bore is a wave phenomenon, induced by a sudden increase of water flow and accompanied by wave trains without any wave breaking. In this study, the propagation of undular bores over a slowly varying topography is investigated numerically, using a fully non-linear Boussinesq model. A finite difference method with predictor-corrector procedure is applied to solve the model. The developments of undular bores on a flat bottom are simulated to show the ability of the model to produce undulations at the head of the bore. Numerical results show that they are in a good agreement with the experimental results. Based on some numerical run, the greater slope led to small undulations, with lower phase velocity. Moreover, for a greater Froude number, the amplitude of undulations increased with faster phase velocity.

Boussinesq-type model, finite difference, small slope, undular bore.