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

Published online by Cambridge University Press:  16 February 2021

Wai Hong Ronald Chan Open the ORCID record for Wai Hong Ronald Chan [Opens in a new window] ,
Perry L. Johnson Open the ORCID record for Perry L. Johnson [Opens in a new window] ,
Parviz Moin Open the ORCID record for Parviz Moin [Opens in a new window]  and
Javier Urzay Open the ORCID record for Javier Urzay [Opens in a new window]
Wai Hong Ronald Chan
Affiliation:
Center for Turbulence Research (CTR), Stanford University, Stanford, CA94305, USA
Perry L. Johnson
Affiliation:
Center for Turbulence Research (CTR), Stanford University, Stanford, CA94305, USA The Henry Samueli School of Engineering, University of California, Irvine, Irvine, CA92697, USA
Parviz Moin*
Affiliation:
Center for Turbulence Research (CTR), Stanford University, Stanford, CA94305, USA
Javier Urzay
Affiliation:
Center for Turbulence Research (CTR), Stanford University, Stanford, CA94305, USA
*
†Email address for correspondence: moin@stanford.edu
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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 (Chan, Johnson & Moin, J. Fluid Mech., vol. 912, 2021, A42) 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 large-scale break-up dynamics is 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.

JFM classification

Multiphase and Particle-laden Flows: Gas/liquid flow Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 912 , 10 April 2021 , A43
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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