Bubble breakup reduced to a one-dimensional nonlinear oscillator

Breaking dynamics of bubbles in turbulence produce a wide range of bubble sizes, which mediates gas transfer, in particular, at the ocean/atmosphere interface. At the scales close to the stability limit of bubbles torn away by inertial forces, a typical geometry that induces bubble breakup is the uniaxial straining flow. In this configuration, the bubble shapes and their limit of stability have been studied theoretically and numerically near their equilibrium. Using numerical simulations, we investigate the bubble dynamics and breakup in such flows, starting from initial shapes far from equilibrium. We show that the breakup threshold is significantly smaller than the previous linear predictions and evidence that the breakup threshold depends on both the Reynolds number at the bubble size, and the initial bubble shape (ellipsoids). To rationalize the bubble dynamics and the observed thresholds, we propose a reduced model for the oblate/prolate oscillations (second Rayleigh mode) based on an effective potential that depends on the control parameters and the initial bubble shape. Our model successfully reproduces bubble oscillations, the maximal deformation below the threshold, and the bubble lifetime above the threshold.