The Connection between Bubble Size Spectra and Energy Dissipation Rates in the Upper Ocean

Garrett, Chris; Li, Ming; Farmer, David M.

doi:10.1175/1520-0485(2000)030<2163:tcbbss>2.0.co;2

Cited by 182 publications

(301 citation statements)

References 18 publications

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“…where γ is the surface tension, ρ the water density and C is a dimensionless constant which has a value of approximately 0.5 (Martinez-Bazan et al 1999;Garrett et al 2000;Deane & Stokes 2002). Several experimental studies (Loewen et al 1996;Terrill et al 2001;Deane & Stokes 2002;Leifer & de Leeuw 2006;Rojas & Loewen 2007;Blenkinsopp & Chaplin 2010) have identified a bubble size distribution following a power law of the bubble radius N (r) ∝ r −m with m ∈ [2.5 : 3.5], roughly compatible with Eq.…”

Section: Bubble Size Distribution Models and Observationssupporting

confidence: 52%

“…Garrett et al (2000) introduced the most widely used model for the bubble size distribution. It relies on a steady model of a turbulent break-up cascade, assuming the size distribution per unit volume N (r), with r the bubble radius, to depend only on the local (time-averaged) turbulent dissipation rateε, the bubble radius r and the source of bubbles, i.e.…”

Section: Bubble Size Distribution Models and Observationsmentioning

confidence: 99%

“…Note that Garrett et al (2000) consider the bubble size distribution per unit volume N (r), which is physically equivalent to N (r) the bubble size distribution (N (r)dr and N (r)dr are respectively the per unit volume, and absolute number of bubbles of radii between r and r + dr). If one considers N (r), Eq.…”

Section: Bubble Size Distribution Models and Observationsmentioning

confidence: 99%

“…Therefore a more complete description of the time evolution of the bubble size distribution during the breaking event and during the rise of the bubbles is needed. Indeed, the model from Garrett et al (2000) (Eq. (1.1)), while undoubtelly correct for constant Q, does not describe the temporal evolution in which the bubble size distribution experiences very rapid change (Terrill et al 2001;Deane & Stokes 2002).…”

Section: Bubble Size Distribution Models and Observationsmentioning

confidence: 99%

“…This model is appealing because it considers only the bubble energy and the turbulent break-up dissipation rate while Garrett et al (2000) had to introduce the constant air flow rate Q to close their dimensional argument. Since this model is adiabatic in time, the measurable time-averaged bubble size distribution N (r) is going to be N (r) ∝ r −2 .…”

Section: Bubble Size Distribution Models and Observationsmentioning

confidence: 99%

See 4 more Smart Citations

Air entrainment and bubble statistics in breaking waves

2016

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We investigate air entrainment and bubble statistics in three-dimensional breaking waves through novel direct numerical simulations of the two-phase air-water flow, resolving the length scales relevant for the bubble formation problem, the capillary length and the Hinze scale. The dissipation due to breaking is found to be in good agreement with previous experimental observations and inertial-scaling arguments. The air-entrainment properties and bubble-size statistics are investigated for various initial characteristic wave slopes. For radii larger than the Hinze scale, the bubble size distribution, can be described by N (r, t) = B(V 0 /2π)(ε(t − ∆τ )/W g)r −10/3 r −2/3 m during the active breaking stages, where ε(t − ∆τ ) is the time dependent turbulent dissipation rate, with ∆τ the collapse time of the initial air pocket entrained by the breaking wave, W a weighted vertical velocity of the bubble plume, r m the maximum bubble radius, g gravity, V 0 the initial volume of air entrained, r the bubble radius and B a dimensionless constant. The active breaking time-averaged bubble size distribution is described bȳ N (r) = B(1/2π)( l L c /W gρ)r −10/3 r −2/3 m , where l is the wave dissipation rate per unit length of breaking crest, ρ the water density and L c the length of breaking crest. Finally, the averaged total volume of entrained air,V , per breaking event can be simply related to l byV = B( l L c /W gρ), which leads to a relationship to a characteristic slope, S, of V ∝ S 5/2 . We propose a phenomenological turbulent bubble break-up model, based on earlier models and the balance between mechanical dissipation and work done against buoyancy forces. The model is consistent with the numerical results and existing experimental results.

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Section: Bubble Size Distribution Models and Observationssupporting

confidence: 52%

Section: Bubble Size Distribution Models and Observationsmentioning

confidence: 99%

Section: Bubble Size Distribution Models and Observationsmentioning

confidence: 99%

Section: Bubble Size Distribution Models and Observationsmentioning

confidence: 99%

Section: Bubble Size Distribution Models and Observationsmentioning

confidence: 99%

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Air entrainment and bubble statistics in breaking waves

2016

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Optical measurements of small deeply penetrating bubble populations generated by breaking waves in the Southern Ocean

Randolph

Dierssen

Twardowski³

et al. 2014

JGR Oceans

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Bubble size distributions ranging from 0.5 to 125 lm radius were measured optically during high winds of 13 m s 21 and large-scale wave breaking as part of the Southern Ocean Gas Exchange Experiment.Very small bubbles with radii less than 60 mm were measured at 6-9 m depth using optical measurements of the near-forward volume scattering function and critical scattering angle for bubbles (80 ). The bubble size distributions generally followed a power law distribution with mean slope values ranging from 3.6 to 4.6. The steeper slopes measured here were consistent with what would be expected near the base of the bubble plume. Bubbles, likely stabilized with organic coatings, were present for time periods on the order of 10-100 s at depths of 6-9 m. Here, relatively young seas, with an inverse wave age of approximately 0.88 and shorter characteristic wave scales, produced lower bubble concentrations, shallower bubble penetration depths, and steep bubble size distribution slopes. Conversely, older seas, with an inverse wave age of 0.70 and longer characteristic wave scales, produced relatively higher bubble concentrations penetrating to 15 m depth, larger bubble sizes, and shallower bubble size distribution slopes. When extrapolated to 4 m depth using a previously published bubble size distribution, our estimates suggest that the deeply penetrating small bubbles measured in the Southern Ocean supplied 36% of the total void fraction and likely contributed to the transfer and supersaturation of low-solubility gases.

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On the seawater temperature dependence of the sea spray aerosol generated by a continuous plunging jet

et al. 2014

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Key Points:• Particle concentrations decreased as seawater temperature increased to ∼9°C • Bubbles with r film < 2 mm decreased as seawater temperature increased to ∼9°C• Particle concentration was correlated with bubble density at the water surface Abstract Breaking waves on the ocean surface produce bubbles which, upon bursting, deliver seawater constituents into the atmosphere as sea spray aerosol particles. One way of investigating this process in the laboratory is to generate a bubble plume by a continuous plunging jet. We performed a series of laboratory experiments to elucidate the role of seawater temperature on aerosol production from artificial seawater free from organic contamination using a plunging jet. The seawater temperature was varied from −1.3• C to 30.1 • C, while the volume of air entrained by the jet, surface bubble size distributions, and size distribution of the aerosol particles produced was monitored. We observed that the volume of air entrained decreased as the seawater temperature was increased. The number of surface bubbles with film radius smaller than 2 mm decreased nonlinearly with seawater temperature. This decrease was coincident with a substantial reduction in particle production. The number concentrations of particles with dry diameter less than ∼1 m decreased substantially as the seawater temperature was increased from −1.3With further increase in seawater temperature (up to 30• C), a small increase in the number concentration of larger particles (dry diameter >∼0.3 m) was observed. Based on these observations, we infer that as seawater temperature increases, the process of bubble fragmentation changes, resulting in decreased air entrainment by the plunging jet, as well as the number of bubbles with film radius smaller than 2 mm. This again results in decreased particle production with increasing seawater temperature.

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The Connection between Bubble Size Spectra and Energy Dissipation Rates in the Upper Ocean

Cited by 182 publications

References 18 publications

Air entrainment and bubble statistics in breaking waves

Air entrainment and bubble statistics in breaking waves

Optical measurements of small deeply penetrating bubble populations generated by breaking waves in the Southern Ocean

On the seawater temperature dependence of the sea spray aerosol generated by a continuous plunging jet

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