Fluttering instability in a liquid sheet with acoustic feedback.

Abstract

This study focuses on a fluttering instability that can affect a falling liquid sheet. Small displacements of the surface of the liquid may be amplified by the Helmholtz instability mechanism, and naturally occurring acoustic feedback in some configurations can lead to sustained oscillations. The fluttering oscillations have been observed in the free-falling water sheets of several dams and artificial waterfalls, and depending on their scale have been considered to be either attractive or objectionable. The author was recently able to conduct detailed experiments on two large waterfall fountains in Dunedin, New Zealand, and many different oscillation modes were observed. In addition to periodic motions, these interesting dynamical systems can exhibit such effects as mode-hopping, hysteresis, and chaotic behavior. This report includes video pictures of these oscillations and the first model describing the small amplitude dynamics of such a system. Numerical solutions of the differential equations are summarized and compared with experimental behavior. The results should make it possible to design large fountains that are not susceptible to the instability, or alternatively to design small systems that exhibit the instability in its most striking forms.