  The pressure-driven inertial collapse of a cylindrical void in an inviscid
liquid is an integrable, Hamiltonian system that forms a finite-time
singularity as the radius of the void collapses to zero. Here it is shown that
when the natural cylindrical symmetry of the void is perturbed azimuthally, the
perturbation modes neither grow nor decay, but instead cause constant amplitude
vibrations about the leading-order symmetric collapse. Though the amplitudes
are frozen in time, they grow relative to the mean radius which is collapsing
to zero, eventually overtaking the leading-order symmetric implosion. Including
weak viscous dissipation destroys the integrability of the underlying symmetric
implosion, and the effect on the stability spectrum is that short-wavelength
disturbances are now erased as the implosion proceeds. Introducing a weak
rotational flow component to the symmetric implosion dynamics causes the
vibrating shapes to spin as the mean radius collapses. The above theoretical
scenario is compared to a closely related experimental realization of void
implosion: the disconnection of an air bubble from an underwater nozzle. There,
the thin neck connecting the bubble to the nozzle implodes primarily radially
inward and disconnects. Recent experiments were able to induce vibrations of
the neck shape by releasing the bubble from a slot-shaped nozzle. The frequency
and amplitude of the observed vibrations are consistent with the theoretical
prediction once surface tension effects are taken into account.
