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Title: Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity

Abstract

Growth of the single-fluid single-mode Rayleigh-Taylor instability (RTI) is revisited in 2D and 3D using fully compressible high-resolution simulations. We conduct a systematic analysis of the effects of perturbation Reynolds number (Rep) and Atwood number (A) on RTI’s late-time growth. Contrary to the common belief that single-mode RTI reaches a terminal bubble velocity, we show that the bubble re-accelerates when Rep is sufficiently large, consistent with [Ramaparabhu et al. 2006, Wei and Livescu 2012]. However, unlike in [Ramaparabhu et al. 2006], we find that for a sufficiently high Rep, the bubble’s late-time acceleration is persistent and does not vanish. Analysis of vorticity dynamics shows a clear correlation between vortices inside the bubble and re-acceleration. Due to symmetry around the bubble and spike (vertical) axes, the self-propagation velocity of vortices points in the vertical direction. If viscosity is sufficiently small, the vortices persist long enough to enter the bubble tip and accelerate the bubble [Wei and Livescu 2012]. A similar effect has also been observed in ablative RTI [Betti and Sanz 2006]. As the spike growth increases relative to that of the bubble at higher A, vorticity production shifts downward, away from the centerline and toward the spike tip. We modifymore » the Betti-Sanz model for bubble velocity by introducing a vorticity efficiency factor η = 0.45 to accurately account for re-acceleration caused by vorticity in the bubble tip. It had been previously suggested that vorticity generation and the associated bubble re-acceleration are suppressed at high A. However, we present evidence that if the large Rep limit is taken first, bubble re-acceleration is still possible. Our results also show that re-acceleration is much easier to occur in 3D than 2D, requiring smaller Rep thresholds.« less

Authors:
 [1];  [1];  [1];  [1]; ORCiD logo [2]
  1. Univ. of Rochester, NY (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Rochester, NY (United States). Lab. for Laser Energetics
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1574757
Alternate Identifier(s):
OSTI ID: 1599478; OSTI ID: 1604426; OSTI ID: 1633508
Report Number(s):
LA-UR-19-26670; 2019-250, 2508, 1552
Journal ID: ISSN 0167-2789; TRN: US2100012
Grant/Contract Number:  
89233218CNA000001; NA0003856; SC0014318; SC002022; SC001932; NA0003914; AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Physica. D, Nonlinear Phenomena
Additional Journal Information:
Journal Volume: 403; Journal Issue: C; Journal ID: ISSN 0167-2789
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; Rayleigh-Taylor instability; nonlinear instability; vorticity; turbulence; Rayleigh-Taylor instability, nonlinear instability, vorticity, turbulence; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Bian, Xin, Aluie, Hussein, Zhao, Dongxiao, Zhang, Huasen, and Livescu, Daniel. Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity. United States: N. p., 2019. Web. doi:10.1016/j.physd.2019.132250.
Bian, Xin, Aluie, Hussein, Zhao, Dongxiao, Zhang, Huasen, & Livescu, Daniel. Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity. United States. doi:https://doi.org/10.1016/j.physd.2019.132250
Bian, Xin, Aluie, Hussein, Zhao, Dongxiao, Zhang, Huasen, and Livescu, Daniel. Mon . "Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity". United States. doi:https://doi.org/10.1016/j.physd.2019.132250. https://www.osti.gov/servlets/purl/1574757.
@article{osti_1574757,
title = {Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity},
author = {Bian, Xin and Aluie, Hussein and Zhao, Dongxiao and Zhang, Huasen and Livescu, Daniel},
abstractNote = {Growth of the single-fluid single-mode Rayleigh-Taylor instability (RTI) is revisited in 2D and 3D using fully compressible high-resolution simulations. We conduct a systematic analysis of the effects of perturbation Reynolds number (Rep) and Atwood number (A) on RTI’s late-time growth. Contrary to the common belief that single-mode RTI reaches a terminal bubble velocity, we show that the bubble re-accelerates when Rep is sufficiently large, consistent with [Ramaparabhu et al. 2006, Wei and Livescu 2012]. However, unlike in [Ramaparabhu et al. 2006], we find that for a sufficiently high Rep, the bubble’s late-time acceleration is persistent and does not vanish. Analysis of vorticity dynamics shows a clear correlation between vortices inside the bubble and re-acceleration. Due to symmetry around the bubble and spike (vertical) axes, the self-propagation velocity of vortices points in the vertical direction. If viscosity is sufficiently small, the vortices persist long enough to enter the bubble tip and accelerate the bubble [Wei and Livescu 2012]. A similar effect has also been observed in ablative RTI [Betti and Sanz 2006]. As the spike growth increases relative to that of the bubble at higher A, vorticity production shifts downward, away from the centerline and toward the spike tip. We modify the Betti-Sanz model for bubble velocity by introducing a vorticity efficiency factor η = 0.45 to accurately account for re-acceleration caused by vorticity in the bubble tip. It had been previously suggested that vorticity generation and the associated bubble re-acceleration are suppressed at high A. However, we present evidence that if the large Rep limit is taken first, bubble re-acceleration is still possible. Our results also show that re-acceleration is much easier to occur in 3D than 2D, requiring smaller Rep thresholds.},
doi = {10.1016/j.physd.2019.132250},
journal = {Physica. D, Nonlinear Phenomena},
number = C,
volume = 403,
place = {United States},
year = {2019},
month = {11}
}

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Works referenced in this record:

Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density
journal, November 1882


Inertial-confinement fusion with lasers
journal, May 2016

  • Betti, R.; Hurricane, O. A.
  • Nature Physics, Vol. 12, Issue 5
  • DOI: 10.1038/nphys3736

Effects of residual kinetic energy on yield degradation and ion temperature asymmetries in inertial confinement fusion implosions
journal, May 2018

  • Woo, K. M.; Betti, R.; Shvarts, D.
  • Physics of Plasmas, Vol. 25, Issue 5
  • DOI: 10.1063/1.5026706

Impact of three-dimensional hot-spot flow asymmetry on ion-temperature measurements in inertial confinement fusion experiments
journal, October 2018

  • Woo, K. M.; Betti, R.; Shvarts, D.
  • Physics of Plasmas, Vol. 25, Issue 10
  • DOI: 10.1063/1.5048429

Supernova 1987A
journal, September 1989


Experimental astrophysics with high power lasers and Z pinches
journal, August 2006

  • Remington, Bruce A.; Drake, R. Paul; Ryutov, Dmitri D.
  • Reviews of Modern Physics, Vol. 78, Issue 3
  • DOI: 10.1103/RevModPhys.78.755

An overview of Rayleigh-Taylor instability
journal, July 1984


New phenomena in variable-density Rayleigh–Taylor turbulence
journal, December 2010


Numerical simulations of two-fluid turbulent mixing at large density ratios and applications to the Rayleigh–Taylor instability
journal, November 2013

  • Livescu, D.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 371, Issue 2003
  • DOI: 10.1098/rsta.2012.0185

Incompressible Rayleigh–Taylor Turbulence
journal, January 2017


Effects of Diffusion on Interface Instability between Gases
journal, January 1962

  • Duff, R. E.; Harlow, F. H.; Hirt, C. W.
  • Physics of Fluids, Vol. 5, Issue 4
  • DOI: 10.1063/1.1706634

Compressibility effects on the Rayleigh–Taylor instability growth between immiscible fluids
journal, January 2004


Compressibility effects on the Rayleigh-Taylor instability between miscible fluids
journal, August 2007


Mathematical model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for viscoelastic fluids
journal, April 2011


Viscous effects on the Rayleigh-Taylor instability with background temperature gradient
journal, July 2016

  • Gerashchenko, S.; Livescu, D.
  • Physics of Plasmas, Vol. 23, Issue 7
  • DOI: 10.1063/1.4959810

On the Instability of Superposed Fluids in a Gravitational Field.
journal, July 1955

  • Layzer, David
  • The Astrophysical Journal, Vol. 122
  • DOI: 10.1086/146048

Modelling turbulent mixing by Rayleigh-Taylor instability
journal, July 1989


Three‐dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability
journal, May 1991

  • Youngs, David L.
  • Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 5
  • DOI: 10.1063/1.858059

Power Laws and Similarity of Rayleigh-Taylor and Richtmyer-Meshkov Mixing Fronts at All Density Ratios
journal, January 1995


Analytical Solutions of Layzer-Type Approach to Unstable Interfacial Fluid Mixing
journal, October 1998


Dimensionality dependence of the Rayleigh–Taylor and Richtmyer–Meshkov instability late-time scaling laws
journal, June 2001

  • Oron, D.; Arazi, L.; Kartoon, D.
  • Physics of Plasmas, Vol. 8, Issue 6
  • DOI: 10.1063/1.1362529

A three-dimensional renormalization group bubble merger model for Rayleigh–Taylor mixing
journal, March 2002

  • Cheng, Baolian; Glimm, J.; Sharp, D. H.
  • Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 12, Issue 2
  • DOI: 10.1063/1.1460942

Modeling of Rayleigh-Taylor mixing using single-fluid models
journal, January 2019

  • Kokkinakis, Ioannis W.; Drikakis, Dimitris; Youngs, David L.
  • Physical Review E, Vol. 99, Issue 1
  • DOI: 10.1103/PhysRevE.99.013104

Progress towards ignition on the National Ignition Facility
journal, July 2013

  • Edwards, M. J.; Patel, P. K.; Lindl, J. D.
  • Physics of Plasmas, Vol. 20, Issue 7
  • DOI: 10.1063/1.4816115

Improving cryogenic deuterium–tritium implosion performance on OMEGA
journal, May 2013

  • Sangster, T. C.; Goncharov, V. N.; Betti, R.
  • Physics of Plasmas, Vol. 20, Issue 5
  • DOI: 10.1063/1.4805088

Effects of local defect growth in direct-drive cryogenic implosions on OMEGA
journal, August 2013

  • Igumenshchev, I. V.; Goncharov, V. N.; Shmayda, W. T.
  • Physics of Plasmas, Vol. 20, Issue 8
  • DOI: 10.1063/1.4818280

Three-dimensional simulations of low foot and high foot implosion experiments on the National Ignition Facility
journal, March 2016

  • Clark, D. S.; Weber, C. R.; Milovich, J. L.
  • Physics of Plasmas, Vol. 23, Issue 5
  • DOI: 10.1063/1.4943527

Bubble Acceleration in the Ablative Rayleigh-Taylor Instability
journal, November 2006


Limits of the potential flow approach to the single-mode Rayleigh-Taylor problem
journal, December 2006


Experimental study of the single-mode three-dimensional Rayleigh-Taylor instability
journal, December 2007

  • Wilkinson, J. P.; Jacobs, J. W.
  • Physics of Fluids, Vol. 19, Issue 12
  • DOI: 10.1063/1.2813548

The late-time dynamics of the single-mode Rayleigh-Taylor instability
journal, July 2012

  • Ramaprabhu, P.; Dimonte, Guy; Woodward, P.
  • Physics of Fluids, Vol. 24, Issue 7
  • DOI: 10.1063/1.4733396

Late-time quadratic growth in single-mode Rayleigh-Taylor instability
journal, October 2012


Three-dimensional single-mode nonlinear ablative Rayleigh-Taylor instability
journal, February 2016

  • Yan, R.; Betti, R.; Sanz, J.
  • Physics of Plasmas, Vol. 23, Issue 2
  • DOI: 10.1063/1.4940917

Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers
journal, January 2018


Self-Similar Multimode Bubble-Front Evolution of the Ablative Rayleigh-Taylor Instability in Two and Three Dimensions
journal, October 2018


Two mode coupling of the ablative Rayleigh-Taylor instabilities
journal, March 2019

  • Xin, J.; Yan, R.; Wan, Z. -H.
  • Physics of Plasmas, Vol. 26, Issue 3
  • DOI: 10.1063/1.5070103

Direct-drive inertial confinement fusion: A review
journal, November 2015

  • Craxton, R. S.; Anderson, K. S.; Boehly, T. R.
  • Physics of Plasmas, Vol. 22, Issue 11
  • DOI: 10.1063/1.4934714

Comprehensive numerical methodology for direct numerical simulations of compressible Rayleigh–Taylor instability
journal, May 2016

  • Reckinger, Scott J.; Livescu, Daniel; Vasilyev, Oleg V.
  • Journal of Computational Physics, Vol. 313
  • DOI: 10.1016/j.jcp.2015.11.002

Effects of isothermal stratification strength on vorticity dynamics for single-mode compressible Rayleigh-Taylor instability
journal, September 2019


Compressible Rayleigh–Taylor turbulent mixing layer between Newtonian miscible fluids
journal, September 2017


Rayleigh–Taylor shock waves
journal, December 2007

  • Olson, Britton J.; Cook, Andrew W.
  • Physics of Fluids, Vol. 19, Issue 12
  • DOI: 10.1063/1.2821907

Inviscid criterion for decomposing scales
journal, May 2018


Baropycnal Work: A Mechanism for Energy Transfer across Scales
journal, May 2019


Decoupled Cascades of Kinetic and Magnetic Energy in Magnetohydrodynamic Turbulence
journal, April 2019


Compact finite difference schemes with spectral-like resolution
journal, November 1992


Transition stages of Rayleigh–Taylor instability between miscible fluids
journal, April 2002


Direct Numerical Simulations of Rayleigh-Taylor instability
journal, December 2011


Turbulence with Large Thermal and Compositional Density Variations
journal, January 2020


Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae
journal, July 2006

  • Cabot, William H.; Cook, Andrew W.
  • Nature Physics, Vol. 2, Issue 8
  • DOI: 10.1038/nphys361

Computations of three‐dimensional Rayleigh–Taylor instability
journal, May 1990

  • Tryggvason, Grétar; Unverdi, Salih Ozen
  • Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 5
  • DOI: 10.1063/1.857717

Buoyancy-driven variable-density turbulence
journal, October 2007