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 bubbles through a Plateau–Rayleigh instability driven through the action of surface tension. Large air cavities produce bubbles through a Rayleigh–Taylor instability driven by gravity and moderated by surface tension, which has a stabilizing effect. Surface tension, interface curvature and gravity are all important for cases between these two extremes. Predicted unstable mode wavenumber and bubble size show good agreement with direct numerical simulations of plunging breaking waves and air cylinders.
Highlights
They showed that the bubble size spectrum resulting from a fragmentation cascade follows a −10/3 power-law scaling with bubble radius, a result that has been demonstrated in laboratory and field observations (Deane & Stokes 2002; Leifer & De Leeuw 2006; Rojas & Loewen 2007; Blenkinsopp & Chaplin 2010) and numerical simulations (Deike, Melville & Popinet 2016; Wang, Yang & Stern 2016; Yu et al 2019; Yu, Hendrickson & Yue 2020; Chan, Johnson & Moin 2021a; Chan et al 2021b; Mostert, Popinet & Deike 2021)
This study investigates the breakup of air filaments and air cavities into bubbles through the unstable growth of interface waves
The dispersion equation for the waves is derived by generalizing the Rayleigh–Taylor instability to cylindrical coordinates with surface tension, surface curvature and gravity force simultaneously accommodated
Summary
Bubbles generated by breaking waves play important roles in many air–sea exchange processes, including sea spray aerosol generation (Modini et al 2013; Veron 2015; DeMott et al 2016; Erinin et al 2019), gas transfer (Banner & Peregrine 1993; Farmer, McNeil & Johnson 1993; Keeling 1993; Melville 1996; Liang et al 2013; Derakhti & Kirby 2014) and the exchange of moisture and heat (Bortkovskii 1987), all of which have significant impacts on weather and global climate. Li & Farmer (2000) argued that relatively large bubbles are entrained initially and are subsequently prone to fragmentation driven by turbulent pressure fluctuations They showed that the bubble size spectrum resulting from a fragmentation cascade follows a −10/3 power-law scaling with bubble radius, a result that has been demonstrated in laboratory and field observations (Deane & Stokes 2002; Leifer & De Leeuw 2006; Rojas & Loewen 2007; Blenkinsopp & Chaplin 2010) and numerical simulations (Deike, Melville & Popinet 2016; Wang, Yang & Stern 2016; Yu et al 2019; Yu, Hendrickson & Yue 2020; Chan, Johnson & Moin 2021a; Chan et al 2021b; Mostert, Popinet & Deike 2021).
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