Stochastic bubble shape oscillations*

In turbulent flows, bubble fate is controlled by the ratio between inertia and capillarity, namely the Weber number, We. There exists a critical Weber number which separates breaking from non-breaking bubbles. However, this limit is only defined in a statistical sense as an a priori stable bubble can encounter a large velocity or pressure fluctuation and break. Using direct numerical simulations of a single bubble in homogeneous and isotropic turbulence, we study bubble shape oscillations as a function of We. We decompose the surface onto the spherical harmonics base and show that the mode stochastic dynamics can be fully described by a damped linear oscillator randomly forced by turbulence. The natural frequency remains unchanged from the quiescent flow case, while the damping factor is significantly larger than in the absence of a surrounding flow. The forcing term is surprisingly independent on We. This model can then be used to predict more accurately bubble lifetimes in turbulent flows.