Edgetones and Nappe Oscillation

Similarities between the mechanisms of edgetones and nappe oscillation (a phenomenon in which a thin sheet of water discharging freely from an overspill weir oscillates violently) are discussed. Attention is drawn to the fact that, for a water nappe subject to harmonically varying transverse air pressures, the elements that deviate farthest from the equilibrium trajectory are not, as might be supposed, those that depart when the pressure reaches its peak value but, in fact, those that depart when the pressure is zero. Important implications of this curious finding are discussed, and it is suggested that the motion of an oscillating nappe system is governed by a differential-difference equation that accounts for instability and hysteretic characteristics and allows for a rational explanation of the transfer of energy from the jet to the vibratory motion. Similar considerations may apply to the instability characteristics of jet-edge systems.