Bubble pinch-off in turbulence
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Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved November 3, 2019 (received for review June 7, 2019)

Significance
As a bubble breaks apart, the final pinching culminates in a singularity. We investigate the pinch-off of a bubble in turbulence and demonstrate that the turbulent flow field freezes during the pinching process, opening the route for a self-similar collapse close to the one predicted for unperturbed configuration. The role of the turbulent flow field is, therefore, to set the complex initial conditions, which can lead to oscillations of the neck shape during the collapse and the eventual escape from self-similarity with the appearance of a kink-like interfacial structure. This work can be seen as a prototype for understanding the route to finite-time singularities in realistic multiscale systems where random perturbations are present, with both fundamental and practical implications.
Abstract
Although bubble pinch-off is an archetype of a dynamical system evolving toward a singularity, it has always been described in idealized theoretical and experimental conditions. Here, we consider bubble pinch-off in a turbulent flow representative of natural conditions in the presence of strong and random perturbations, combining laboratory experiments, numerical simulations, and theoretical modeling. We show that the turbulence sets the initial conditions for pinch-off, namely the initial bubble shape and flow field, but after the pinch-off starts, the turbulent time at the neck scale becomes much slower than the pinching dynamics: The turbulence freezes. We show that the average neck size,
Footnotes
- ↵1To whom correspondence may be addressed. Email: ldeike{at}princeton.edu.
Author contributions: D.J.R. and L.D. designed research; D.J.R., W.M., S.P., and L.D. performed research; D.J.R., W.M., and L.D. analyzed data; and D.J.R., W.M., S.P., and L.D. wrote the paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
Data deposition: Data and code to reproduce plots are available at http://arks.princeton.edu/ark:/88435/dsp014f16c5691.
This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1909842116/-/DCSupplemental.
- Copyright © 2019 the Author(s). Published by PNAS.
This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).
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