Abstract:Air filaments and cavities in plunging breaking waves, generically cylinders, produce bubbles through an interface instability. The effects of gravity, surface tension and surface curvature on cylinder breakup are explored. A generalized dispersion relation is obtained that spans the Rayleigh–Taylor and Plateau–Rayleigh instabilities as cylinder radius varies. The analysis provides insight into the role of surface tension in the formation of bubbles from filaments and cavities. Small filaments break up into bu… Show more
“…Garrett, Li & Farmer (2000) proposed that, for bubbles larger than the Hinze scale, a power-law scaling N(d) ∝ d −10/3 describes the steady-state bubble size distribution, assuming that the break-up rate scales with the turbulent frequency at the bubble size. This regime has since been reported in several experiments (Deane & Stokes 2002;Rojas & Loewen 2007;Blenkinsopp & Chaplin 2010) and simulations (Deike, Melville & Popinet 2016;Wang, Yang & Stern 2016;Soligo, Roccon & Soldati 2019;Chan et al 2021;Gao, Deane & Shen 2021;Rivière et al 2021;Mostert, Popinet & Deike 2022). For smaller bubbles, the size distribution typically exhibits a shallower slope (Deane & Stokes 2002;Blenkinsopp & Chaplin 2010), with fewer studies resolving this range of scales and some variation in the values that have been reported.…”
Section: Bubble Break-up In Turbulencesupporting
confidence: 57%
“…This regime has since been reported in several experiments (Deane & Stokes 2002; Rojas & Loewen 2007; Blenkinsopp & Chaplin 2010) and simulations (Deike, Melville & Popinet 2016; Wang, Yang & Stern 2016; Soligo, Roccon & Soldati 2019; Chan et al. 2021; Gao, Deane & Shen 2021; Rivière et al. 2021; Mostert, Popinet & Deike 2022).…”
We present experiments on large air cavities spanning a wide range of sizes relative to the Hinze scale
$d_{H}$
, the scale at which turbulent stresses are balanced by surface tension, disintegrating in turbulence. For cavities with initial sizes
$d_0$
much larger than
$d_{H}$
(probing up to
$d_0/d_{H} = 8.3$
), the size distribution of bubbles smaller than
$d_{H}$
follows
$N(d) \propto d^{-3/2}$
, with
$d$
the bubble diameter. The capillary instability of ligaments involved in the deformation of the large bubbles is shown visually to be responsible for the creation of the small bubbles. Turning to dynamical, three-dimensional measurements of individual break-up events, we describe the break-up child size distribution and the number of child bubbles formed as a function of
$d_0/d_{H}$
. Then, to model the evolution of a population of bubbles produced by turbulent bubble break-up, we propose a population balance framework in which break-up involves two physical processes: an inertial deformation to the parent bubble that sets the size of large child bubbles, and a capillary instability that sets the size of small child bubbles. A Monte Carlo approach is used to construct the child size distribution, with simulated stochastic break-ups constrained by our experimental measurements and the understanding of the role of capillarity in small bubble production. This approach reproduces the experimental time evolution of the bubble size distribution during the disintegration of large air cavities in turbulence.
“…Garrett, Li & Farmer (2000) proposed that, for bubbles larger than the Hinze scale, a power-law scaling N(d) ∝ d −10/3 describes the steady-state bubble size distribution, assuming that the break-up rate scales with the turbulent frequency at the bubble size. This regime has since been reported in several experiments (Deane & Stokes 2002;Rojas & Loewen 2007;Blenkinsopp & Chaplin 2010) and simulations (Deike, Melville & Popinet 2016;Wang, Yang & Stern 2016;Soligo, Roccon & Soldati 2019;Chan et al 2021;Gao, Deane & Shen 2021;Rivière et al 2021;Mostert, Popinet & Deike 2022). For smaller bubbles, the size distribution typically exhibits a shallower slope (Deane & Stokes 2002;Blenkinsopp & Chaplin 2010), with fewer studies resolving this range of scales and some variation in the values that have been reported.…”
Section: Bubble Break-up In Turbulencesupporting
confidence: 57%
“…This regime has since been reported in several experiments (Deane & Stokes 2002; Rojas & Loewen 2007; Blenkinsopp & Chaplin 2010) and simulations (Deike, Melville & Popinet 2016; Wang, Yang & Stern 2016; Soligo, Roccon & Soldati 2019; Chan et al. 2021; Gao, Deane & Shen 2021; Rivière et al. 2021; Mostert, Popinet & Deike 2022).…”
We present experiments on large air cavities spanning a wide range of sizes relative to the Hinze scale
$d_{H}$
, the scale at which turbulent stresses are balanced by surface tension, disintegrating in turbulence. For cavities with initial sizes
$d_0$
much larger than
$d_{H}$
(probing up to
$d_0/d_{H} = 8.3$
), the size distribution of bubbles smaller than
$d_{H}$
follows
$N(d) \propto d^{-3/2}$
, with
$d$
the bubble diameter. The capillary instability of ligaments involved in the deformation of the large bubbles is shown visually to be responsible for the creation of the small bubbles. Turning to dynamical, three-dimensional measurements of individual break-up events, we describe the break-up child size distribution and the number of child bubbles formed as a function of
$d_0/d_{H}$
. Then, to model the evolution of a population of bubbles produced by turbulent bubble break-up, we propose a population balance framework in which break-up involves two physical processes: an inertial deformation to the parent bubble that sets the size of large child bubbles, and a capillary instability that sets the size of small child bubbles. A Monte Carlo approach is used to construct the child size distribution, with simulated stochastic break-ups constrained by our experimental measurements and the understanding of the role of capillarity in small bubble production. This approach reproduces the experimental time evolution of the bubble size distribution during the disintegration of large air cavities in turbulence.
“…Finally, the air bubbles reach the upper water surface and degas, whereas the thin filaments break into tiny bubbles. This is a clear manifestation of the Rayleigh-Taylor instability mechanism involving gravity and surface tension (Gao, Deane & Shen 2021b).…”
Section: Air Entrainment and Bubbles Distributionmentioning
confidence: 85%
“…Finally, the air bubbles reach the upper water surface and degas, whereas the thin filaments break into tiny bubbles. This is a clear manifestation of the Rayleigh–Taylor instability mechanism involving gravity and surface tension (Gao, Deane & Shen 2021 b ). Figure 12.Details of the fragmentation of the cylindrical air cavity in numerical simulation of wave breaking at (3D1E4f).…”
Section: Numerical Simulation Of Wave Breakingmentioning
The flow generated by the breaking of free-surface waves in a periodic domain is simulated numerically with a gas–liquid Navier–Stokes solver. The solver relies on the volume-of-fluid method to account for different phases, and the interface tracking is carried out by using novel schemes based on a tailored total-variation-diminishing limiter. The numerical solver is proved to be characterized by a low numerical dissipation, thanks to the use of a scheme that guarantees energy conservation in the discrete form. Both two- and three-dimensional simulations have been performed, and the analysis is presented in terms of energy dissipation, air entrainment, bubble fragmentation, statistics and distribution. Particular attention is paid to the analysis of the mechanisms of viscous dissipation. To this purpose, coherent vortical structures, such as vortex tubes and vortex sheets, are identified, and the different behaviours of the vortex sheets and tubes at various Reynolds numbers are highlighted. The correlation between vortical structures and energy dissipation demonstrates clearly their close link both in the mixing zone and in the pure water domain, where the coherent structures propagate as a consequence of the downward transport. Notably, it is found that the dissipation is identified primarily by the vortex sheets, whereas the vortex tubes govern mainly the intermittency.
“…Admittedly, we have assumed that the wave surface elevation is a single‐valued function, which may not be true when wave breaking occurs. However, to address this issue, high‐resolution observational data (e.g., Deane & Stokes, 2002; Erinin et al., 2019; Veron et al., 2012) or computationally expensive multi‐phase simulations (e.g., Gao et al., 2021; Tang et al., 2017) are needed to provide the hydrodynamic information of breaking waves, sprays and bubbles, which is beyond the scope of this study. Finally, we remark that our framework can be easily extended to more general parameter settings.…”
The downwelling irradiance is a crucial part of the air‐sea heat flux and a major energy source for the photosynthesis processes in the upper ocean. The modeling of the irradiance field is often time‐consuming in conventional Monte Carlo (MC) simulations. We propose an accelerated model based on machine learning to significantly reduce the computational cost. By introducing a generalized beam spreading function, we transform the raw data generated with the MC simulation into training data of reduced dimensions, which is then used to develop an artificial neural network. To validate the machine learning model, we use the MC model to simulate the irradiance field under a broadband wave field. For both clear and turbid seawater, the irradiance field predicted by the machine learning model agrees well with the MC simulation result. Compared with the MC simulation that is computationally expensive, our machine learning model is O(1,000) times faster.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
