Air Entraining Bubbly Flows Driven by Strong Free-Surface Turbulence
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Author(s)
Gaylo, Declan B.
Advisor(s)
Yue, Dick K.P.
Date Issued
February 2026
Publisher
Massachusetts Institute of Technology
Abstract
Bubbles beneath turbulent free surfaces are ubiquitous in natural and engineering processes, where predicting their size distribution is of fundamental importance. Examples include air-sea gas exchange and bubble acoustics. The bubble size distribution N(a), where a is radius, is governed by the population balance equation (PBE), which has a term for each mechanism that evolves the bubble population. We consider fragmentation, entrainment, and degassing. These mechanisms are driven by turbulence near the surface, but predicting free-surface turbulence (FST) is a challenge for models, e.g., Reynolds-averaged Navier-Stokes (RANS). We use direct numerical simulation (DNS) to resolve FST. We show that turbulent Froude numbers Fr²=ε/uᵣₘₛg>0.1 delineate strong FST, where near-surface turbulence is isotropic. We provide a robust definition of surface layer thickness δₛ, which collapses relevant metrics within the surface layer. For strong FST, free-surface effects are restricted to the surface layer. Towards a surface layer model for RANS, we elucidate the scaling of δₛ and energy flux into the surface layer.
While DNS resolves turbulence, measuring bubble evolution mechanisms is a challenge. We develop Eulerian label advection (ELA) to provide accurate volume-conserving bubble tracking regardless of evolution complexity. ELA allows the first direct measurement of evolution mechanisms in DNS of FST. For fragmentation, we verify that it can be treated as memoryless (assumed by the PBE) and quantify the timescale to reach N(a)∝a^-10/3, the equilibrium for fragmentation-dominated bubble populations. From DNS of multiple FST flows, we show the large-bubble entrainment size distribution I(a) scales with Fr⁶ and a^-14/3, consistent with a mechanism we describe. We obtain the degassing rate Λ(a), which has turbulence-driven and buoyancy-driven regimes with different scalings. We find that FST is degassing, not fragmentation, dominated, and derive the corresponding equilibrium bubble population, N(a)=I(a)/Λ(a), which agrees with DNS measurements. Compared to N(a)∝a^-10/3, this distinct new equilibrium has two power-law regimes, fewer large bubbles, and is very sensitive to Froude number.
The findings of this thesis contribute to fundamental understanding of strong FST and the size distribution of bubbles within it, and help pave the way for modeling and application of these flows.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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