Non-linear oscillations of fluid in a container

Abstract

This paper is concerned with forced oscillations of fluid in a rectangular container. From the linearized approximation of the equations governing these oscillations, resonance frequencies are obtained for which the amplitude of the oscillations becomes infinite. Observation shows that under these circumstances a hydraulic jump is formed, which travels periodically back and forth between the walls of the container. This hydraulic jump is a non-linear phenomenon, analogous to the shock wave appearing in one-dimensional gas flow under similar resonance conditions.A theory developed by previous authors for one-dimensional gas flow is applied to the fluid oscillations in order to calculate the strength and the phase of the jump. The moment exerted on the container is also calculated. These quantities were measured experimentally at the lowest resonance frequency and the results are in good agreement with the theoretical values.