Leonardo da Vinci’s bubble paradox popped

Scientists in Spain and the UK have have discovered a mechanism to explain the unstable movement of bubbles rising in water.
Five centuries ago, renaissance artist and scientist Leonardo da Vinci observed that rising air bubbles, if large enough, periodically deviate from a direct vertical trajectory by zigzagging or spiralling. However, no quantitative description of the phenomenon or physical mechanism to explain this motion had ever been found
Miguel Ángel Herrada, professor of aerospace engineering and fluid mechanics at the University of Sevilla, and Jens Eggers, professor of applied mathematics at the University of Bristol, have now discovered a mechanism to explain the unstable movement of bubbles rising in water. According to the researchers, the results may be useful in understanding the motion of particles whose behaviour is between a solid and a gas.

They have developed a numerical technique to characterise precisely the air-water interface of a bubble, which enables them to simulate its motion and explore its stability. In a paper published in the journal PNAS, the authors describe how their simulations closely match high-precision measurements of unsteady bubble motion and show that bubbles deviate from a straight trajectory in water when their spherical radius exceeds 0.926mm.
The researchers propose a mechanism for the instability of the bubble trajectory, whereby periodic tilting of the bubble changes its curvature. This affects the upward velocity, causing a wobble in the bubble’s trajectory.
As the fluid moves faster and the fluid pressure falls around the high-curvature surface, the pressure imbalance returns the bubble to its original position, restarting the periodic cycle.