NUMERICAL COMPUTATIONS OF 2-DIMENSIONAL SOLITARY WAVES GENERATED BY MOVING DISTURBANCES

Two-dimensional solitary waves generated by disturbances moving near t he critical speed in shallow water are computed by a time-stepping pro cedure combined with a desingularized boundary integral method for irr otational flow. The fully non-linear kinematic and dynamic free-surfac e boundary conditions and the exact rigid body surface condition are e mployed. Three types of moving disturbances are considered: a pressure on the free surface, a change in bottom topography and a submerged cy linder. The results for the free surface pressure are compared to the results computed using a lower-dimensional model, i.e. the forced Kort eweg-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, th e fully non-linear model predicts larger solitons than the fKdV equati on. The fully non-linear calculations show that a free surface pressur e generates significantly larger waves than that for a bottom bump wit h 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.