Waves caused by a moving disturbance in a shallow channel of finite width

Abstract

The flow created by an impulsively started pressure distribution travelling at a constant velocity in a shallow channel is investigated. The restricted Green-Naghdi theory of fluid sheets is used to perform the three-dimensional calculations. The results show remarkable similarity to model tests. In particular, these calculations predict the periodic generation of two-dimensional solitons in front of and travelling faster than the disturbance if the disturbance is large enough. Behind the disturbance a complicated, doubly corrugated set of waves is formed. The computations also predict that periodic creation of solitons is accompanied by a correspondingly periodic oscillation of the wave drag, as well as a dramatic increase in the mean wave drag.