Scott Russell's wave generator

In this paper we study the dynamics of a system consisting of a heavy box s inking vertically into water. The classic configuration is due to Scott Rus sell who used the sinking box in 1844 to illustrate the formation of a soli tary wave in a long rectangular tank. We use a combination of computer simu lation and experiment to clarify details of the wave formation and the dyna mics of the sinking box. We find that as the box sinks the water is heaved up to form both the solitary wave and a reverse plunging wave which forms a vortex. This vortex follows the wave down the tank. The computer simulatio n uses the particle method smoothed particle hydrodynamics (SPH) which allo ws us to follow the formation of the waves and the dynamics of the box. The simulation results are in satisfactory agreement with the experiments. We derive scaling relations for the velocity of the box and for the amplitude of the solitary wave. These scaling relations are in reasonable agreement w ith the experiments and the simulations. (C) 2000 American Institute of Phy sics. [S1070-6631(00)01703-7].