On large-amplitude pulsating fountains

We study the behaviour of an upward vertical water jet of density, rho, and surface tension, a, injected through a tube of diameter, D, with a momentum-averaged velocity, V. These fountains are shown to exhibit large-amplitude oscillations in the range 0.1 less than or equal to D/a less than or equal to 1.6, and 20 less than or equal to V-2/(gD) less than or equal to 400, where g is the acceleration due to gravity and a is the capillary length, a = (2 sigma/(rho g))(1/2). The characteristic frequency of the oscillations, f, and their limits of existence are studied experimentally. A model is developed, leading to the expression for the frequency: f = g/3V. This expression is shown to be in good agreement with existing data and with new measurements, conducted over a wide range of Bond (Bo = D/a) and Froude (Fr = V-2/gD) numbers. The stability of the model is considered and the limits of the oscillatory regime are related to the hydrodynamic properties of the flow.