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Breaking waves generate a distribution of bubble sizes that evolves overtime. Knowledge of how this distribution evolves is of practical importance formaritime and climate studies. The analytical framework developed in Part 1examined how this evolution is governed by the bubble-mass flux from large tosmall bubble sizes, which depends on the rate of break-up events and thedistribution of child bubble sizes. These statistics are measured in Part 2 asensemble-averaged functions of time by simulating ensembles of breaking waves,and identifying and tracking individual bubbles and their break-up events. Thebreak-up dynamics are seen to be statistically unsteady, and two intervals withdistinct characteristics were identified. In the first interval, thedissipation rate and bubble-mass flux are quasi-steady, and the theoreticalanalysis of Part 1 is supported by all observed statistics, including theexpected -10/3 power-law exponent for the super-Hinze-scale size distribution.Strong locality is observed in the corresponding bubble-mass flux, supportingthe presence of a super-Hinze-scale break-up cascade. In the second interval,the dissipation rate decays, and the bubble-mass flux increases as small- andintermediate-sized bubbles become more populous. This flux remains stronglylocal with cascade-like behaviour, but the dominant power-law exponent for thesize distribution increases to -8/3 as small bubbles are also depleted morequickly. This suggests the emergence of different physical mechanisms duringdifferent phases of the breaking-wave evolution, although size-local break-upremains a dominant theme. Parts 1 and 2 present an analytical toolkit forpopulation balance analysis in two-phase flows.

The turbulent bubble break-up cascade. Part 2. Numerical simulations of breaking waves