The origin of the tubular jet

Abstract

A vertical cylindrical tube is partially immersed in a water-filled container and pressurized to lower the fluid level inside the tube. A sudden release of the pressure in the tube creates a singularity on top of the rising free surface. At the very beginning of the process a jet emerges at the centre of the surface, the strength of which strongly depends on the initial shape of the meniscus. Here, the time-evolution of the complex shape of the free surface and the flow around the cylindrical tube are analysed using high-speed imaging, particle image velocimetry, and numerical simulations. The tubular jet is found to be created by the following series of events, which eventually lead to the flow focusing at the tube's centre. A circular surface wave, produced by the funnelling of flow into the tube, is pushed inwards by the radial flow directly underneath the surface. As the wave moves inward and eventually collapses at the centre of the tube, a bump of fluid grows in the centre due to the converging flow in the bulk. This converging flow continues to feed the jet after the circular wave has collapsed. The singularity of the wave collapse is manifested in the initial sharp tip of the jet. All of the above events are traced back to a single origin: the convergence of the flow as it enters the tube. Movies are available with the online version of the paper.