The stability of a falling sheet of water

Abstract

Experiments were made on thin sheets of water projected vertically downwards from a slit between side walls. Three kinds of self-induced disturbance were investigated. (i) If the water fell into a pool and air was confined by a back wall behind the sheet, oscillations were set up of the type sometimes seen at a weir across a river. They could be diminished or stopped by splitters inserted at the slit to form A-shaped breaks in the sheet so that resonance between the sheet and the trapped air was reduced. Complete suppression was difficult to achieve unless the obstruction was made unacceptably large; it is better to allow the stream to fall unimpeded on to some kind of bridge structure placed above the pool and permitting free access of air to the space behind. A few readings were taken with the sheet projected horizontally, thus simulating flow over a weir more closely. (ii) With the back wall removed and a sufficient height of fall, the sheet developed irregular oscillations and abruptly disintegrated. This effect was largely caused by reaction with the surrounding air, for it did not occur when the experiment was repeated in a vacuum chamber. (iii) If the velocity of projection from the slit was diminished below that of antisymmetri-cal waves, a continuous sheet was impossible and the water emerged in streams. The V-shaped sheet was examined that was formed when the discharge was reduced sufficiently for contact with the side walls to be lost. The wavelength of the stationary train of ripples that appeared above the edges of the sheet was found to be given by the usual theory which assumes gravity to be negligible compared with surface tension.