Open Channel Flow Near The Resonance Speed.

Abstract

Flows in an open channel with either corrugated side walls or a corrugated bottom, possess critical speeds at or near which the prediction of either the free surface wave or the internal wave by linear approximation fails. However, if the nonlinear terms in Euler equation and boundary conditions are kept, a finite amplitude of the free surface wave or the internal wave can then be determined. In this dissertation, three different open-channel flows of an inviscid liquid, which may be stratified, are studied, and the amplitude of either the free surface wave or the internal wave is successfully determined to be of the order of the one-third power of the amplitude of the corrugation of the side walls or of the bottom.