Instability and chaotic behaviour in a free-surface flow

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Abstract
This paper describes some experimental observations of free-surface flows arising when fluid is poured over the end of a flat plate into a reservoir well below the plate. This class of flows was found to be highly unstable with over seven hundred qualitatively different flows being observed in the experiment. At very small values of the flux the liquid fell from the plate into the reservoir in the form of droplets which developed periodically at a number of sites on the underside of the plate. As the flux was increased these 'sites’ were able to sustain continuous, unbroken streams, and combinations of drip sites and continuous streams were possible. At still larger values of the flux there was a tendency for the liquid to fall in 'sheets’ and several combinations of’ sheet flows’ and continuous streams were observed, some of which flows exhibited a rather chaotic temporal behaviour. At even larger flux values the flow resembled that of the classic waterfall, but here there were also some unexpected instabilities where the attachment line of the free surface of the liquid with the plate developed corrugations.