| Abstract: | Two-dimensional solitary waves generated by disturbances moving near the critical speed in shallow water are computed by a time-stepping procedure combined with a desingularized boundary integral method for irrotational flow. The fully non-linear kinematic and dynamic free-surface boundary conditions and the exact rigid body surface condition are employed. Three types of moving disturbances are considered: a pressure on the free surface, a change in bottom topography and a submerged cylinder. The results for the free surface pressure are compared to the results computed using a lower-dimensional model, i.e. the forced Korteweg–de Vries (fKdV) equation. The fully non-linear model predicts the upstream runaway solitons for all three types of disturbances moving near the critical speed. The predictions agree with those by the fKdV equation for a weak pressure disturbance. For a strong disturbance, the fully non-linear model predicts larger solitons than the fKdV equation. The fully non-linear calculations show that a free surface pressure generates significantly larger waves than that for a bottom bump with an identical non-dimensional forcing function in the fKdV equation. These waves can be very steep and break either upstream or downstream of the disturbance. |
