Gravity Waves and Solitons

Abstract

A Scottish engineer in the mid nineteenth century John Scott Russell built a 30′ wave tank in his backyard. Dropping a weight at one end of the channel produced a solitary gravity wave with speed c = √ g(h + a) where h is the height of undisturbed water in the channel, a is the wave amplitude, and g is the acceleration of gravity. He observed a compound wave which split into two with the larger one racing ahead of the smaller. Wave pools in amusement parks operate on a similar principle, using a plunger at one end of pool, blowing air on surface at one end, or dumping a large volume of water at one end.