WEAKLY NON-LINEAR EFFECTS OF FLOW OF A STRATIFIED FLUID ON MOTION OF SHEAR WAVES

When water is withdrawn from a stratfied reservoir, the ow at low discharges is confined to a narrow layer adjacent to the level of the sink. This phenomenon, known as selective withdrawal, has widespread applications in lake and reservoir water quality management. It is known that the formation of a selective withdrawal layer is due to the motion of internal waves called shear waves" from the reservoir outlet to the upstream. The ow becomes steady when the shear waves are either blocked by the inertia of the background ow or damped by viscosity. In this paper, with the assumption of a small reservoir discharge, the weakly nonlinear effects of the reservoir ow on the motion of shear waves are investigated. A multi-scale perturbation technique is used to solve the governing equations. The results indicate that shear wave speeds are reduced by the background ow.