Curvature singularity in the asymmetric breakup of an underwater air bubble

The presence of slight azimuthal asymmetry in the initial shape of an underwater bubble entirely alters the final breakup dynamics. Here, I examine the influence of initial asymmetry on the final breakup by simulating the bubble surface evolution as a Hamiltonian evolution corresponding to an inviscid, two-dimensional, planar implosion. I find two types of breakups: a previously reported coalescence mode in which distant regions along the air-water surface curve inwards and eventually collide with finite speed, and a hitherto uncharacterized cusp-like mode where the surface develops sharp tips whose radii of curvature are much smaller than the average neck radius. I present three sets of results that characterize the nature of this cusp mode. First, I show that the cusp-like mode corresponds to a phase space trajectory that passes close to a saddle-node structure. In other words, an evolution towards a cross-section shape with sharp tips invariably later evolves away from it. In phase space, this saddle-n...