Effect of Bottom Irregularities on Small Amplitude Shallow Water Waves

Abstract

Behavior of finite amplitude long gravity waves in a water layer with an irregular bottom surface is investigated by means of a nonlinear perturbation method. Under the assumption that the irregularities are of small size, a simple set of nonlinear equations is presented. There arise two effects in the propagation characteristic of shallow water waves, change in phase velocity and damping of amplitude. For the one-dimensional and unidirectional motion of shallow water waves the set of equations is reduced to a simpler one, the generalized Korteweg-de Vries equation. The decay rate of a solitary wave is also obtained.