On large-amplitude pulsating fountains

We study the behaviour of an upward vertical water jet of density, ρ, and surface tension, σ, 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 ≤ D/a ≤ 1.6, and 20 ≤ V²/(gD) ≤ 400, where g is the acceleration due to gravity and a is the capillary length, a = (2σ/(pg))^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: [equation presented] 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 ≡ V²/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.