On large-amplitude pulsating fountains

Abstract

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[les ]D/a[les ]1.6, and 20[les ]V2/(gD)[les ]400, where g is the acceleration due to gravity and a is the capillary length, a≡(2σ/(ρg))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:formula hereThis 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.