Generation of solitary waves by forward- and backward-step bottom forcing

A finite difference method based on the Euler equations is developed for co mputing waves and wave resistance due to different bottom topographies movi ng steadily at the critical velocity in shallow water. A two-dimensional sy mmetric and slowly varying bottom topography, as a forcing for wave generat ion, call be viewed as a combination of fore and aft parts. For a positive topography (a bump), the fore part is a forward-step forcing, which contrib utes to the generation of upstream-advancing solitary waves, whereas the af t part is a backward-step forcing to which a depressed water surface region and a trailing wavetrain are attributed. These two wave systems respective ly radiate upstream and downstream without mutual interaction. For a negative topography (a hollow), the fore part is a backward step and the aft part is a forward step. The downstream-radiating waves generated by the backward-step forcing at the fore part will interact with the upstream -running waves generated by the forward-step forcing at the aft. Therefore, the wave system generated bq a negative topography is quite different from that by a positive topography. The generation period of solitary waves is slightly longer and the instantaneous drag fluctuation is skewed for a nega tive topography. When the length of the negative topography increases, the oscillation of the wave-resistance coefficient with time does not coincide with the period of solitary wave emission.