Oceanic bubble size distributions: capillarity produces the tiny bubbles

Bubbles entrained by breaking waves modulate mass exchanges at the ocean-atmosphere interface. Below a critical size called the Kolmogorov-Hinze scale, a bubble’s shape is maintained by surface tension, and turbulent inertial forces can no longer break it. These small bubbles, of size ranging from microns to millimeters, are the main contributors to mass fluxes such as the dissolution of low solubility gases and sea spray produced by bubble bursting. While their presence in the upper ocean has long been acknowledged, the physical mechanism controlling the size distribution of sub-Hinze bubbles has not previously been understood.

Releasing a large pocket of gas in a turbulent flow, both experimentally and numerically, we show that the number density of sub-Hinze bubbles consistently scales as d^-3/2, with d the bubble diameter. This scaling law holds for a sufficiently large-scale separation between the initial bubble size and the Kolmogorov-Hinze scale. We further show that sub-Hinze child bubble production, and thus the observed scaling law, is controlled by capillarity. Specifically, the strong deformation of large super-Hinze bubbles produces filaments that pinch apart into tiny bubbles on a timescale controlled by the Rayleigh-Plateau instability. Using a population model, we eventually link fates of individual breaking bubbles to the size distribution of sub-Hinze bubbles.