Decompression, self-leveling, and wobble decay of bubble rings released by scuba divers

Scuba divers blow bubble rings, hollow vortex rings with a gas core that expands as the ring rises because the water pressure drops with every meter of ascent. Classical theory keeps the gas volume fixed and treats only level rings, and the one earlier estimate of the expansion, for a laboratory tank, found it small. Here the ring is modeled as a thin hollow vortex ring with a core that obeys Boyle's law and a motion set by the Kelvin impulse balance of a massless bubble, and this planar model is tested against a 3D vortex filament model. The ring radius has an exact solution in exponential integrals that holds for any tilt, and the extra growth relative to a ring of constant gas volume depends on a single release pressure number. This gain is near one in a tank but reaches 1.38 for release at 10 m and 1.98 at 40 m. A reference ring holding 10 mL of gas and released at 10 m grows from 5 to 18.5 cm in radius, compared with 14.8 cm at constant volume. Because its horizontal impulse is conserved, a tilted ring levels faster than predicted for a core that carries axial flow; a ring released 30 degrees from level ends nearly level after drifting 1.44 m sideways. Long bending waves decay as the ring grows. Along these trajectories, a viscous capillary stability criterion limits intact ascent to release depths of about 10 m. The two models agree to the expected order in the core slenderness.