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Stability of a falling water sheet is studied by measuring the displacements of water surface at the various heights of the sheet. Effects of geometry at the backward space of the sheet and disturbance generated at the upstream water surface are investigated from the power spectrum of the data. Experiment without a vertical wall at the backward of the sheet reveals that the oscillation occurs due to the shear instability of air flow. This oscillation with frequency about 10 Hz at the upstream and 20 Hz at the downstream seems to be caused by a resonance of the system, because these frequencies are amplified along the sheet as elucidated from the forced oscillation experiment.The modulation of the oscillations observed by the vertical wall experiment, which is known as the nappe oscillation, is examined and predicted by a model derived from present study. In addition, the shear wave appearing on the sheet and leading to the sheet break-up is discussed by a linear stability analyses of the Navier-Stokes equation.

Incipient oscillations of a falling water sheet and their instability mechanisms