Journal
JOURNAL OF FLUID MECHANICS
Volume 917, Issue -, Pages -Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2021.333
Keywords
bubble dynamics; breakup; coalescence
Categories
Funding
- U.S. Office of Naval Research [N00014-20-1-2059]
- Department of Defense High Performance Computing Modernization Program
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This study focuses on the evolution of the bulk bubble-size distribution under the influence of turbulence-induced fragmentation and free-surface entrainment, finding two regimes based on the entrainment distribution dependence. The weak injection regime is independent of the entrainment distribution, while the strong injection regime's power-law slope is determined by gamma.
We consider the evolution of the bulk bubble-size distribution N(a, t) of large bubbles (Weber number We >> 1) under free-surface entrainment described generally by an entrainment size distribution I(a) with power-law slope gamma and large-radius cutoff a(max). Our main focus is the interaction between turbulence-driven fragmentation and free-surface entrainment, and, for simplicity, we ignore other mechanisms such as degassing, coalescence and dissolution. Of special interest are the equilibrium bulk distribution N-eq(a), with local power-law slope (beta) over tilde (eq)(a), and the time scale tau(c) to reach this equilibrium after initiation of entrainment. For bubble radii a << a(max), we find two regimes for the dependence of N-eq(a) on the entrainment distribution. There is a weak injection regime for gamma >= -4, where (beta) over tilde (eq)(a) = -10/3 independent of the entrainment distribution; and a strong injection regime for gamma < -4, where the power-law slope depends on gamma and is given by <(beta)over tilde>(eq) = gamma + 2/3. The weak regime provides a general explanation for the commonly observed -10/3 power law originally proposed by Garrett et al. (J. Phys. Oceanogr., vol. 30 (9), 2000, pp. 2163-2171), and suggests that different weak entrainment mechanisms can all lead to this result. For a similar to a(max), we find that N-eq(a) exhibits a steepening deviation from a power law due to fragmentation and entrainment, similar to what has been observed, but here absent other mechanisms such as degassing. The evolution of N(a, t) to N-eq(a) is characterised by the critical time tau(c) proportional to C-f epsilon(-1/3) a(max)(2/3), where epsilon is the turbulence dissipation rate and C-f is a new constant that quantifies the dependence on the daughter size distribution in a fragmentation event. For typical breaking waves, tc can be quite small, limiting the time t less than or similar to tau(c) when direct measurement of N(a, t) might provide information about the underlying entrainment size distribution.
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