Stability of Water Bells Generated by Jet Impacts on a Disk

Water bells appear when a cylindrical liquid jet impacts normally onto a disk of similar diameter. First observed and described experimentally by F. Savart, their stationary shape was analytically obtained by J. Boussinesq. Here we consider the stability of these bells and derive a general stability criterion showing their sensitivity both to the pressure difference across the liquid sheet and to the ejection angle from the impacting disk. In this later case, we find a critical angle of ejection above which the bell is periodically destroyed and created.