Degassing-dominated bubble populations in air-entraining free-surface turbulence

The size distribution of bubbles created by air entrainment at a free surface is important to a variety of natural and engineering applications. In addition to entrainment, fragmentation and degassing of bubbles are relevant physical mechanisms. When fragmentation is dominant, Garret et al. (J. Phys. Oceanogr., vol. 30, 2000) predict a -10/3 power law for the bubble size distribution of large Weber number, We, bubbles. This power law is ubiquitous in breaking waves. Here, we study entrainment by free surface turbulence (FST) where, unlike breaking waves, the energy to entrain bubbles comes directly from turbulence beneath the free surface. We perform direct numerical simulation (DNS) of a canonical FST flow at a range of Froude number, Fr, to study the relative effects of fragmentation versus degassing during active air entrainment. Even at We>>1 when we expect fragmentation to be strongest, we find the effect of degassing is dominate over fragmentation. We develop a theory to predict the power law of the bubble size distribution under degassing dominance, which agrees with DNS results. This distribution is distinct from the fragmentation-dominated distribution in two ways. First, two regimes of bubble degassing in turbulence lead to a split power law, with a critical bubble radius scaling with Fr and Reynolds number Re. Second, in both regimes the power law is more negative (fewer large bubbles) than -10/3. We discuss what measures, in addition to the power-law of the bubble size distribution, can be used to determine if a given air entraining flow is fragmentation or degassing dominated.