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Title: A solution to Rayleigh-Taylor instabilities. Bubbles, spikes, and their scalings

Journal Article · · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
 [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
+ Show Author Affiliations

A fluid that pushes on and accelerates a heavier fluid, small perturbations at their interface grows with time and lead. to turbulent mixing. The same instability, known as the Rayleigh-Taylor instability, operates when a heavy fluid is supported by a lighter fluid in a gravitational field. Moreover, it has a particularly deleterious effect on inertial-confinement-fusion implosions and is known to operate over 18 orders of magnitude in dimension. We propose analytic expressions for the bubble and spike amplitudes and mixing widths in the linear, nonlinear, and turbulent regimes. They cover arbitrary density ratios and accelerations that are constant or changing relatively slowly with time. Here, we discuss their scalings and compare them with simulations and experiments.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1237525
Report Number(s):
LLNL-JRNL-636376
Journal Information:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Vol. 89, Issue 5; ISSN 1539-3755
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 25 works
Citation information provided by
Web of Science

References (24)

Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories journal February 2000
Effect of viscosity on Rayleigh-Taylor and Richtmyer-Meshkov instabilities journal January 1993
Three-dimensional Rayleigh-Taylor instability Part 2. Experiment journal February 1988
Analytical Model of Nonlinear, Single-Mode, Classical Rayleigh-Taylor Instability at Arbitrary Atwood Numbers journal March 2002
Limitations and failures of the Layzer model for hydrodynamic instabilities journal July 2008
Hot-spot mix in ignition-scale implosions on the NIF journal May 2012
Analytic Approach to Nonlinear Rayleigh-Taylor and Richtmyer-Meshkov Instabilities journal January 1998
The late-time dynamics of the single-mode Rayleigh-Taylor instability journal July 2012
Experimental investigation of turbulent mixing by Rayleigh-Taylor instability journal July 1984
Rayleigh–Taylor and shear driven mixing with an unstable thermal stratification journal October 1994
Vortex simulations of the Rayleigh–Taylor instability journal January 1980
Power Laws and Similarity of Rayleigh-Taylor and Richtmyer-Meshkov Mixing Fronts at All Density Ratios journal January 1995
Rayleigh-Taylor Instability of an Ultrathin Foil Accelerated by the Radiation Pressure of an Intense Laser journal May 2012
Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations journal January 2010
A comparative study of the turbulent Rayleigh–Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration journal May 2004
Turbulent Rayleigh-Taylor instability experiments with variable acceleration journal October 1996
Experimental study of Rayleigh–Taylor instability with a complex initial perturbation journal March 2009
Experimental investigation of RayleighTaylor mixing at small Atwood numbers journal January 1999
Feedback from Central Black Holes in Elliptical Galaxies: Two-Dimensional Models Compared to One-Dimensional Models journal July 2011
Analytical Solutions of Layzer-Type Approach to Unstable Interfacial Fluid Mixing journal October 1998
The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I journal March 1950
Production of reproducible Rayleigh–Taylor instabilities journal October 1979
Numerical simulations of the Rayleigh-Taylor instability journal April 1988
On the Instability of Superposed Fluids in a Gravitational Field. journal July 1955

Cited By (5)

Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime journal January 2018
Direct simulation Monte Carlo investigation of hydrodynamic instabilities in gases
  • Gallis, M. A.; Koehler, T. P.; Torczynski, J. R.
  • 30TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS: RGD 30, AIP Conference Proceedings https://doi.org/10.1063/1.4967552
conference January 2016
The physics of long- and intermediate-wavelength asymmetries of the hot spot: Compression hydrodynamics and energetics journal October 2017
Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities journal August 2019
From ICF to laboratory astrophysics: ablative and classical Rayleigh–Taylor instability experiments in turbulent-like regimes journal December 2018

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