Explosion of chaotic bubbling

We have studied a saddle-node bifurcation/explosion of air bubble formation driven by a sound wave, whose amplitude is the control parameter. The bubbles are formed in a nozzle submerged in a water/glycerol solution inside a cylindrical tube, and the sound wave is tuned to the air column above the fluid. The nonlinear interaction between sound wave and the fluid oscillations, caused by the air bubbles passage through the liquid, results in a route to chaos via quasi-periodicity, with some resonant states characterized by the rational winding numbers W=fs/fb, where fs is the sound wave frequency and fb is the bubbling rate. We also have shown that the bubble dynamics is similar to the one observed in the two-dimensional circle map.