Numerical computations of two‐dimensional solitary waves generated by moving disturbances

Abstract

AbstractTwo‐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.