Abstract
From the similarity theorem, an expression of bubble population is derived as a function of the air entrainment rate, the turbulent kinetic energy (TKE) spectrum density and the surface tension. The bubble size spectrum that we obtain has a dependence of \(a^{ - 2.5 + n_d } \) on the bubble radius, in which n d is positive and dependent on the form of TKE spectrum within the viscous dissipation range. To relate the bubble population with wave parameters, an expression about the air entrainment rate is deduced by introducing two statistical relations to wave breaking. The bubble population vertical distribution is also derived, based on two assumptions from two typical observation results.
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References
Stramski D. Gas Microbubbles: An Assessment of their Significance to Light Scattering in Quiescent Seas. In: Jaffe J S, ed. Ocean Optics XII. Washington: Int Soc for Opt Eng, Bellingham, 1994. 704–710
Stramski D, Tegowski J. Effects of Intermittent Entrainment of Air Bubbles by Breaking. J Geophys Res, 2001, 106: 31345–31360
Pumphery H C, Crum L A. Acoustic Emissions Associated with Drop Impacts. In: Kerman B R, ed. Sea Surface. Dordrecht: Kluwer Academic Publishers, 1988. 151–172
Lu N Q, Prosperetti A, Yoon S W. Underwater Noise Emissions from Bubble Clouds. IEEE J Ocean Engineering, 1990, 15: 275–281
Yoon S W, Crum L A, Properetti A et al. An investigation of the collective oscillations of a bubble cloud. J Acoust Soc Am, 1991, 89:700–706
Woolf D K, Thorpe S A. Bubbles and the air-sea exchange of gases in near-saturation conditions. J Mar Res, 1991, 49: 435–466
Thorpe S A. Some factors affecting the size distribution of ocean bubbles. J Phys Oceanogr, 1992, 22: 382–389
Medwin H. In situ acoustic measurements of bubble populations in coastal waters. J Geophys Res, 1970, 75: 599–611
Thorpe S A. On the clouds of bubbles formed by breaking wind-waves in deep water, and their role in air-sea gas transfer. Phil Trans R Soc Lond, 1982, A304: 155–210
Farmer D M, Vagle S. On the determination of breaking surface wave distributions using ambient sound. J Geophys Res, 1988, 93:3591–3600
Farmer D M, Vagle S, Booth A D. A free-flooding acoustical resonator for measurement of bubble size distribution. J Atmos Oceanic Tech, 1998, 15: 1132–1146
Terrill E J, Melville W K. A broadband acoustic technique for measuring bubble size distribution:laboratory and shallow water measurements. J Atmos Oceanic Tech, 2000, 17: 220–239
Garrett C, Li M, Farmer D. The connection between bubble size spectra and energy dissipation rates in the upper ocean. J Phys Oceanogr, 2000, 30: 2163–2171
Deane G B, Stokes M D. Scale Dependence of Bubble Creation Mechanisms in Breaking Waves. Nature, 2002, 418: 839–844
Terrill E J, Melville W K, Stramski D. Bubble entrainment by breaking waves and their influence on optical scattering in the upper ocean. J Geophys Res, 2001, 106(C8): 16815–16823
Hwang P A, Hsu Y H L, Wu J. Air bubbles produced by breaking wind waves: a laboratory study. J Phys Oceanogr, 1990, 20: 19–28
Haines M A, Johnson B D. Injected bubble in seawater and freshwater measured by a photographic method. J Geophys Res., 1995, 100:7057–7068
Blanchard D C, Woodcock A H. Bubble formation and modification in the sea and its meteorological significance. Tellus, 1957, 9: 145–158
Monahan E C, Zietlow C R. Laboratory comparisons of freshwater and saltwater whitecaps. J Geophys Res, 1969, 74: 6961–6966
Kolovayev P A. Investigation of the concentration and statistical size distribution of wind-produced bubbles in the near-surface ocean layer. Oceanol Engl Thans, 1976, 15: 659–661
Johnson B D, Cooke R C. Bubblepopulations and Spectra in Coastal Water:a Photographic Approach. J Geophys Res, 1979, 84:3761–3766
Cipriano R, Blanchard D C. Bubble and aerosol spectra produced by a laboratory breaking wave. J Geophys Res, 1981, 86: 8085–8092
Broecker H Ch, Siems W. The role of bubbles for gas transfer from water to air at higher wind speeds. Experiments in the wind-wave facility in Hamburg. In: Brutsaert W, Jirka G H, eds. Gas Transfer at Water Surfaces. Norwell: D. Reidel, 1984. 229–236
Baldy S. Bubbles in the close vicinity of breaking waves:statistical characteristics of the generation and dispersion mechanism. J Geophys Res, 1988, 92: 2919–2929
Medwin H, Breitz N D. Ambient and transient bubble spectral densities in Quiescent Seas and under spilling breakers. J Geophys Res, 1989, 94: 12751–12759
Rapp R J, Melville W K. Laboratory measurements of deep-water breaking waves. Phil Trans R Soc London, 1990, A331: 735–800
Scott J C. The role of salt in whitecap persistance. Deep-Sea Research, 1975, 22: 653–657
Baldy S. A generation-dispersion model of ambient and transient bubbles in the close vicinity of breaking wave. J Geophys Res, 1993, 98: 18277–18293
Kolmogorov A N. Energy dissipation in locally isotropic turbulence. Doklady AN SSSR, 1941, 32: 19–21
Paka V T, Nabatov V N, Lozovatsky I D, et al. Oceanic microstructure measurements by “Baklan” and “Grif”. J Atmos Oceanic Tech, 1999, 16(11): 1519–1532
Yuan Y, Hua F, Huang N E et al. A new statistical model for breaking wave. Oceanol Limnol Sin (in Chinese), 1993, 24: 577–583
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Han, L., Yuan, Y. Bubble size distribution in surface wave breaking entraining process. SCI CHINA SER D 50, 1754–1760 (2007). https://doi.org/10.1007/s11430-007-0116-7
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DOI: https://doi.org/10.1007/s11430-007-0116-7