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