Collapse and pinch-off of a non-axisymmetric impact-created air cavity in water

Abstract

The axisymmetric collapse of a cylindrical air cavity in water follows a universal power law with logarithmic corrections. Nonetheless, it has been suggested that the introduction of a small azimuthal disturbance induces a long term memory effect, reflecting in oscillations which are no longer universal but remember the initial condition. In this work, we create non-axisymmetric air cavities by driving a metal disc through an initially-quiescent water surface and observe their subsequent gravity-induced collapse. The cavities are characterized by azimuthal harmonic disturbances with a single mode number m and amplitude a m . For small initial distortion amplitude (1 or 2 % of the mean disc radius), the cavity walls oscillate linearly during collapse, with nearly constant amplitude and increasing frequency. As the amplitude is increased, higher harmonics are triggered in the oscillations and we observe more complex pinch-off modes. For small amplitude disturbances we compare our experimental results with the model for the amplitude of the oscillations by Schmidt et al. (2009) and the model for the collapse of an axisymmetric impact-created cavity previously proposed by Bergmann et al. (2009b). By combining these two models we can reconstruct the three-dimensional shape of the cavity at any time before pinch-off. IntroductionThe pinch-off of an axisymmetric air cavity in water is characterized by a finite-time singularity. The kinetic energy of the flow is focused into a vanishing small volume with a velocity whose magnitude diverges as the pinch-off moment is approached. Several experimental and theoretical scenarios have been recently considered in the study of this problem: a bubble rising from a capillary . Depending on the case, the collapse might be initiated by surface tension, external flow, or hydrostatic pressure. However, irrespective of the cause, towards the end it is the inertia of the fluid that takes over in every case, and the collapse is accelerated as the radius of the cavity shrinks.The time it takes each of these systems to reach the inertial collapse regime varies by orders of magnitude . Hence, it was not an easy task to determine whether there was indeed a universal behaviour underlying this phenomenon. The first proposed model was a power law where the radius decreased proportionally to the arXiv:1109.5823v2 [physics.flu-dyn]

Curvature singularity in the asymmetric breakup of an underwater air bubble

“…There are evidences 15,17,[19][20][21] supporting that for some initial conditions, the interface develops high curvature regions followed by re-entrant water fingers. Using simulations with boundary integral method, I found that, starting with one single mode perturbation, there .…”

“…For experiments studying the collapse of a non-axisymmetric, impact-created air cavity in water [19][20][21] , the initial length scale (∼ cm) is larger compared with bubble breakup experiments while the initial velocity scale there is similar (∼ m/s). Hence for cavity collapse experiments, if the curvature singularity were to form, air compressibility will be the major mechanism to regularize the curvature singularity.…”

“…This can be achieved by either starting with a largely distorted cross-section shape, or using the same perturbation amplitude but a higher vibrational mode n for the initial single mode perturbation. Experiments using initial perturbations with higher mode number n (with n up to 20) have been done by Enriquez et al [19][20][21] . Their experiments focus on the collapse of a non-axisymmetric cavity created by the impact of a disk.…”

“…This idea successfully describes several breakup scenarios, such as water drops break up in air [8][9][10][11][12] . However, recent studies reported that there are breakups which remember their initial states [13][14][15][16][17][18][19][20][21] .…”

Explosions at the water surface

“…And we marginally expect cavities in the regime of low Reynolds and small Bond numbers. Apart from spheres, the impact of discs has also been studied (Bergmann et al 2010), as well as non-axisymmetric objects (Enriquez et al 2010(Enriquez et al , 2012.…”