Gravity–capillary jet-like surface waves generated by an underwater bubble

Abstract

Jet-like surface waves generated by an electric-spark-generated underwater bubble are experimentally studied. Three different motions of jet-like surface waves are observed depending on the inception position of the bubble ($d$: 0.28–7 mm) below the free surface and the maximum radius of the bubble ($R_{m}$: 1.5–3.6 mm). When $d/R_{m}>1.3$, the surface wave shows a simple smooth hump (case 1). When $0.82<d/R_{m}<1.3$, a single droplet or multiple droplets are pinched off sequentially or simultaneously at the tip or from some points of the jet-like surface wave (case 2). Finally, when $d/R_{m}<0.82$, a series of squirting and jetting phenomena are observed at the top of the jet-like surface wave (case 3). For case 1, a proportional relationship is found between $\unicode[STIX]{x1D70C}gh/\unicode[STIX]{x0394}p$ and $(d/R_{m})^{-4.4}$, where $\unicode[STIX]{x1D70C}$ is the density of the fluid, $g$ is the gravitational acceleration and $\unicode[STIX]{x0394}p$ is the difference between the reference atmospheric pressure and the vapour pressure inside a bubble. This proportional relationship is explained semi-analytically using a scaling argument and conservation of momentum and energy, with the help of the Kelvin impulse theory. In addition, we solve the relevant axisymmetric Cauchy–Poisson problem where the initial condition is a jet-like surface wave near its maximum height. By comparing the analytical wave solution with the observed surface wave pattern, it is found that the resultant surface waves are indeed gravity–capillary waves where both the gravity and the surface tension are equally important.

Jetting in finite-amplitude, free, capillary-gravity waves

“…They did not discuss the application of their results to jetting or comment on the presence of critical points due to triadic resonant interactions. A more recent linearised IVP approach has been the study by Kang & Cho (2019) which has experimentally investigated capillary-gravity waves from the bursting of a bubble underwater. The analytical part of this study was confined to the linearised regime viz.…”

Numerical and experimental investigation into the dynamics of a bubble-free-surface system

“…Both collapse and surface jets were found to be dependent on the interbubble distance and the bubble depth below the free surface. Kang and Cho [27] studied the evolution of the free surface following its interaction with a spark-generated bubble and proposed a relationship for the height of the surface jet when the interaction is weak (i.e., at large dimensionless bubble-surface distances, where the free surface deforms without breaking up).…”

“…In the present study, we characterize the evolution of the liquid jets at the free surface for timescales that extend beyond those of the oscillating bubble. The systems that are considered correspond to the "intermediate" regime [27], where the bubble oscillates without bursting at the surface, but the interaction is strong enough so as to induce atomization of the free surface at a later stage. As previously mentioned, past studies were mostly focusing on the dynamics of the bubble and were limited to its first few oscillation cycles.…”

An analysis of surface breakup induced by laser-generated cavitation bubbles in a turbulent liquid jet

“…Although the use of a doublet lens already reduced pulse-to-pulse plasma fluctuations (Tian et al 2019), some shape and size variation of the bubbles were still inevitable for the reasons stated above. Based on knowledge of bubble-induced breakup of flat free surfaces and laminar liquid jets, the size of the bubble and the distance between the bubble and the surface affect the characteristics of the breakup, such as structure and jetting speed (Blake and Gibson 1981;Chahine 1977;Kang and Cho 2019;Patrascioiu et al 2014a, b;Robert et al 2007;Robinson et al 2001;Supponen et al 2015;Zhang et al 2016). Therefore, shot-to-shot variations of the lasergenerated cavitation bubbles in turbulent jets for this study was expected to result in variation of the bubble-induced breakup of the jet.…”

“…The interface can attain a variety of shapes depending on the specific application. Fundamental studies often focus on the bubble collapse event close to a flat free surface (Bempedelis et al 2020;Blake and Gibson 1981;Chahine 1977;Kang and Cho 2019;Patrascioiu et al 2014a, b;Robinson et al 2001;Supponen et al 2015;Zhang et al 2016). Remarkable experimentation on cavitation bubble collapse within a liquid droplet was done in microgravity (Obreschkow et al 2006).…”