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arXiv · 2009.04804

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

Wai Hong Ronald Chan·Perry L. Johnson·Parviz Moin·Javier Urzay
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Abstract

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

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Wai Hong Ronald Chan, Perry L. Johnson, Parviz Moin, Javier Urzay. 2020-09-10. The turbulent bubble break-up cascade. Part 2. Numerical simulations of breaking waves. https://doi.org/10.1017/jfm.2020.1084

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