A three-dimensional renormalization group bubble merger model for Rayleigh-Taylor mixing

Chaos
Baolian ChengDavid H Sharp

Abstract

In this paper we formulate a model for the merger of bubbles at the edge of an unstable acceleration driven (Rayleigh-Taylor) mixing layer. Steady acceleration defines a self-similar mixing process, with a time-dependent inverse cascade of structures of increasing size. The time evolution is itself a renormalization group (RNG) evolution, and so the large time asymptotics define a RNG fixed point. We solve the model introduced here at this fixed point. The model predicts the growth rate of a Rayleigh-Taylor chaotic fluid mixing layer. The model has three main components: the velocity of a single bubble in this unstable flow regime, an envelope velocity, which describes collective excitations in the mixing region, and a merger process, which drives an inverse cascade, with a steady increase of bubble size. The present model differs from an earlier two-dimensional (2-D) merger model in several important ways. Beyond the extension of the model to three dimensions, the present model contains one phenomenological parameter, the variance of the bubble radii at fixed time. The model also predicts several experimental numbers: the bubble mixing rate, alpha(b)=h(b)/Agt(2) approximately 0.05-0.06, the mean bubble radius, and the bubble h...Continue Reading

References

Oct 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·G Dimonte, M Schneider
Apr 30, 1990·Physical Review Letters·J Glimm, D H Sharp

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Citations

Jul 10, 2010·Proceedings of the National Academy of Sciences of the United States of America·Hyunkyung LimDavid H Sharp
Oct 23, 2013·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·James GlimmHyunkyung Lim
Jul 13, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Guy Dimonte
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Arindam BanerjeeMalcolm J Andrews
Feb 20, 2019·Physical Review. E·Ioannis W KokkinakisDavid L Youngs
Feb 18, 2017·Physical Review. E·V RanaD H Sharp
Jun 29, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Xinfeng LiuJ Glimm
Feb 3, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Timothy T Clark, Ye Zhou
Feb 21, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Erwin GeorgeXinfeng Liu
Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Baolian Cheng, A J Scannapieco
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sung-Ik Sohn

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