Scale separation and dependence of entrainment bubble-size distribution in free-surface turbulence

Abstract

We consider the size spectrum of entrained bubbles under strong free-surface turbulence (SFST). We investigate the entrainment bubble-size spectrum per unit (mean) interface area, , with dimension length, and develop a physical/mechanistic model for through energy arguments. The model obtains two distinct regimes of , separated by bubble-size scale. For bubble radius r-{0}]>, the effects of gravity dominate those of the surface tension force , and , where is the turbulence dissipation rate. For and