Fig. 4: Ring bubble translational dynamics.

A During the movement of ring, due to the oscillation and decay of the circulation and radius, its speed also oscillates and decays. B Under different tube, energy increases, speed increases. C Comparison between experimental ring bubble velocity and theoretical predictions by Fukumoto and Saffman. While early equilibrium velocities align well with predictions, deviations occur in initial velocity estimates due to temporal and spatial resolution limitations. The model consistently overestimates long-distance velocities due to inadequate dissipation of circulation. D The velocity and decay model of the vortex ring in a long period of time, the decay is fast in early stage and relatively stable in later stage. E The impulse of ring at different energies and the theoretical maximum travel distance. F Overlay of high-speed camera images showing the trajectory of a ring bubble migrating horizontally within a long transparent tube (details in Supplementary Fig. S15). G Translational distances (d_m) of ring bubbles at different energy outputs for three states. H Migration velocity (u_m) of ring bubbles as a function of migration distance, illustrating velocity attenuation over time for different migration directions. I Displacement of ring bubbles under varying migration directions, indicating minimal horizontal drift compared to vertical migration. J Under different tube, energy increases, the Reynold number of vortex ring increases. K The Weber number. L The cavitation number. M Sequential generation of multiple ring bubbles at 8 ms intervals (E_out = 5.2 J). N The voltage (V), current (I), and sound pressure (P) signals for multiple ring generation. the uniform spacing between multiple peaks indicates excellent repeatability in pulsed generation. O Energy efficiency of bubbles, the energy efficiencies of ring bubble are the ratio between ring and primary bubble. Scale bars, 10 mm. Source data are provided as a Source Data file.