Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II

Zhou, Ye

doi:10.1016/j.physrep.2017.07.008

Title: Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II

Abstract

Rayleigh–Taylor (RT) and Richtmyer–Meshkov(RM) instabilities are well-known pathways towards turbulent mixing layers, in many cases characterized by significant mass and species exchange across the mixing layers (Zhou, 2017. Physics Reports, 720–722, 1–136). Mathematically, the pathway to turbulent mixing requires that the initial interface be multimodal, to permit cross-mode coupling leading to turbulence. Practically speaking, it is difficult to experimentally produce a non-multi-mode initial interface. Numerous methods and approaches have been developed to describe the late, multimodal, turbulent stages of RT and RM mixing layers. This paper first presents the initial condition dependence of RT mixing layers, and introduces parameters that are used to evaluate the level of “mixedness” and “mixed mass” within the layers, as well as the dependence on density differences, as well as the characteristic anisotropy of this acceleration-driven flow, emphasizing some of the key differences between the two-dimensional and three-dimensional RT mixing layers.

Authors:

Zhou, Ye ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: 2017-09-27

Research Org.:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1569184

Report Number(s):: LLNL-JRNL-751112
Journal ID: ISSN 0370-1573; 936444; TRN: US2100266

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: Physics Reports

Additional Journal Information:: Journal Volume: 723-725; Journal Issue: C; Journal ID: ISSN 0370-1573

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Rayleigh–Taylor instability; Richtmyer–Meshkov instability; Kelvin–Helmholtz instability; Shock waves; Transition; Turbulence; Mixing; Astrophysical fluid dynamics; SuperNovae; Inertial confinement fusion (ICF); High energy density physics (HEDP); Direct numerical simulations (DNS); Large-eddy simulations (LES)

Citation Formats


                    Zhou, Ye. Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II.  United States: N. p., 2017. 
Web.  doi:10.1016/j.physrep.2017.07.008.

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                    Zhou, Ye. Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II.  United States.  https://doi.org/10.1016/j.physrep.2017.07.008

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                    Zhou, Ye. Wed .  
"Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II".  United States.  https://doi.org/10.1016/j.physrep.2017.07.008.  https://www.osti.gov/servlets/purl/1569184.

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@article{osti_1569184,

  title        = {Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II},

  author       = {Zhou, Ye},

  abstractNote = {Rayleigh–Taylor (RT) and Richtmyer–Meshkov(RM) instabilities are well-known pathways towards turbulent mixing layers, in many cases characterized by significant mass and species exchange across the mixing layers (Zhou, 2017. Physics Reports, 720–722, 1–136). Mathematically, the pathway to turbulent mixing requires that the initial interface be multimodal, to permit cross-mode coupling leading to turbulence. Practically speaking, it is difficult to experimentally produce a non-multi-mode initial interface. Numerous methods and approaches have been developed to describe the late, multimodal, turbulent stages of RT and RM mixing layers. This paper first presents the initial condition dependence of RT mixing layers, and introduces parameters that are used to evaluate the level of “mixedness” and “mixed mass” within the layers, as well as the dependence on density differences, as well as the characteristic anisotropy of this acceleration-driven flow, emphasizing some of the key differences between the two-dimensional and three-dimensional RT mixing layers.},

  doi          = {10.1016/j.physrep.2017.07.008},

  journal      = {Physics Reports},

  number       = C,

  volume       = 723-725,

  place        = {United States},

  year         = {2017},

  month        = {9}

}

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Fig. 9.1: (Figure 13 of Ramaprabhu et al., 2005, J. Fluid Mech. with permission). Effect of $k$⟨$h$_$k$0⟩: (a) Evolution of bubble amplitude, $h$_$b$ for three cases with long wavelengths present in the initial conditions; (b) Evolution of bubble amplitude, $h$_$b$ for mode-coupling cases.

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Numerical study of the ablative Richtmyer–Meshkov instability of laser-irradiated deuterium and deuterium-tritium targets
journal, November 2010

Marocchino, Alberto; Atzeni, Stefano; Schiavi, Angelo
Physics of Plasmas, Vol. 17, Issue 11
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Evidence for a Bubble-Competition Regime in Indirectly Driven Ablative Rayleigh-Taylor Instability Experiments on the NIF
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Martinez, D. A.; Smalyuk, V. A.; Kane, J. O.
Physical Review Letters, Vol. 114, Issue 21
DOI: 10.1103/PhysRevLett.114.215004

Stabilizing Effect of Anisotropic Thermal Diffusion on the Ablative Rayleigh-Taylor Instability
journal, June 2007

Masse, L.
Physical Review Letters, Vol. 98, Issue 24
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Rayleigh-Taylor Stability of Compressible and Incompressible Radiation-Supported Surfaces and Slabs: Application to QSO Clouds
journal, May 1977

Mathews, William G.; Blumenthal, George R.
The Astrophysical Journal, Vol. 214
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Renormalization group approach to interfacial motion in incompressible Richtmyer-Meshkov instability
journal, September 2010

Matsuoka, Chihiro
Physical Review E, Vol. 82, Issue 3
DOI: 10.1103/PhysRevE.82.036320

Fully nonlinear evolution of a cylindrical vortex sheet in incompressible Richtmyer–Meshkov instability
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Matsuoka, Chihiro; Nishihara, Katsunobu
Physical Review E, Vol. 73, Issue 5
DOI: 10.1103/PhysRevE.73.055304

Analytical and numerical study on a vortex sheet in incompressible Richtmyer-Meshkov instability in cylindrical geometry
journal, December 2006

Matsuoka, Chihiro; Nishihara, Katsunobu
Physical Review E, Vol. 74, Issue 6
DOI: 10.1103/PhysRevE.74.066303

OMEGA EP high-energy petawatt laser: progress and prospects
journal, May 2008

Maywar, D. N.; Kelly, J. H.; Waxer, L. J.
Journal of Physics: Conference Series, Vol. 112, Issue 3
DOI: 10.1088/1742-6596/112/3/032007

Computational parametric study of a Richtmyer-Meshkov instability for an inclined interface
journal, August 2011

McFarland, Jacob A.; Greenough, Jeffrey A.; Ranjan, Devesh
Physical Review E, Vol. 84, Issue 2
DOI: 10.1103/PhysRevE.84.026303

Investigation of the initial perturbation amplitude for the inclined interface Richtmyer–Meshkov instability
journal, July 2013

McFarland, J. A.; Greenough, J. A.; Ranjan, D.
Physica Scripta, Vol. T155
DOI: 10.1088/0031-8949/2013/T155/014014

Experimental investigation of the inclined interface Richtmyer–Meshkov instability before and after reshock
journal, December 2013

McFarland, Jacob; Reilly, David; Creel, Skylar
Experiments in Fluids, Vol. 55, Issue 1
DOI: 10.1007/s00348-013-1640-1

Simulations and Analysis of the Reshocked Inclined Interface Richtmyer–Meshkov Instability for Linear and Nonlinear Interface Perturbations
journal, May 2014

McFarland, Jacob A.; Greenough, Jeffrey A.; Ranjan, Devesh
Journal of Fluids Engineering, Vol. 136, Issue 7
DOI: 10.1115/1.4026858

Large-eddy simulation of Rayleigh-Taylor turbulence with compressible miscible fluids
journal, July 2005

Mellado, J. P.; Sarkar, S.; Zhou, Y.
Physics of Fluids, Vol. 17, Issue 7
DOI: 10.1063/1.1965130

A survey of the mean turbulent field closure models.
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Mellor, George L.; Herring, H. James
AIAA Journal, Vol. 11, Issue 5
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Development of a turbulence closure model for geophysical fluid problems
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Mellor, George L.; Yamada, Tetsuji
Reviews of Geophysics, Vol. 20, Issue 4
DOI: 10.1029/RG020i004p00851

Sensitivity of inertial confinement fusion hot spot properties to the deuterium-tritium fuel adiabat
journal, February 2015

Melvin, J.; Lim, H.; Rana, V.
Physics of Plasmas, Vol. 22, Issue 2
DOI: 10.1063/1.4908278

Numerical simulation of the aerobreakup of a water droplet
journal, November 2017

Meng, Jomela C.; Colonius, Tim
Journal of Fluid Mechanics, Vol. 835
DOI: 10.1017/jfm.2017.804

Title: Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II

Abstract

Citation Formats

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Extensible component-based architecture for FLASH, a massively parallel, multiphysics simulation code journal, October 2009

Analysis of the effects of energy deposition on shock-driven turbulent mixing journal, July 2013

A review of the ablative stabilization of the Rayleigh–Taylor instability in regimes relevant to inertial confinement fusion journal, May 1994

Modal model for the nonlinear multimode Rayleigh–Taylor instability journal, August 1996

Diagnostics hardening for harsh environment in Laser Mégajoule (invited) journal, October 2008

High-Energy-Density Physics at the National Ignition Facility journal, October 2017

The dynamics of shock accelerated light and heavy gas cylinders journal, September 1993

Development of Richtmyer–Meshkov and Rayleigh–Taylor instability in the presence of magnetic field journal, October 2011

Vorticity generation by shock propagation through bubbles in a gas journal, April 1988

Dynamics of buoyancy-driven flows at moderately high Atwood numbers journal, April 2016

Supernova mechanisms journal, October 1990

On the identification of a vortex journal, February 1995

Small amplitude theory of Richtmyer–Meshkov instability journal, May 1994

The nonlinear large-eddy simulation method applied to Sc≈1 and Sc⪢1 passive-scalar mixing journal, March 2008

Two-equation and multi-fluid turbulence models for Rayleigh–Taylor mixing journal, December 2015

Anisotropy in turbulent flows and in turbulent transport journal, July 2005

Dynamical evolution of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts journal, September 2002

Initial conditions and modeling for simulations of shock driven turbulent material mixing journal, June 2017

M IXING E FFICIENCY IN S TRATIFIED S HEAR F LOWS journal, January 2003

Simulation ensemble for a laser–driven shear experiment journal, September 2013

Richtmyer–Meshkov instability with strong radiatively driven shocks journal, February 1996

Experimental study of Rayleigh–Taylor instability with a complex initial perturbation journal, March 2009

Laser-driven compression of hollow shells: power requirements and stability limitations journal, February 1976

Eddy damping, backscatter, and subgrid stresses in subgrid modeling of turbulence journal, June 1991

On the control and suppression of the Rayleigh-Taylor instability using electric fields journal, February 2014

The National Ignition Facility journal, May 2001

First steps in modelling turbulence and its origins: a commentary on Reynolds (1895) ‘On the dynamical theory of incompressible viscous fluids and the determination of the criterion’ journal, April 2015

Rayleigh–Taylor instability of a continuously stratified fluid under a general rotation field journal, July 1989

On hot-wire diagnostics in Rayleigh–Taylor mixing layers journal, March 2009

Effect of shock proximity on Richtmyer–Meshkov growth journal, May 2003

Rayleigh–Taylor instability in nonlinear Schrödinger flow journal, July 2012

Spike morphology in blast-wave-driven instability experiments journal, May 2010

The effects that changes in the diaphragm aperture have on the resulting shock tube flow journal, April 2012

Spike Penetration in Blast-Wave-Driven Instabilities journal, December 2011

Theory of the Rayleigh-Taylor instability journal, August 1991

Effects of shear flow and transverse magnetic field on Richtmyer–Meshkov instability journal, January 2008

A turbulent mixing Reynolds stress model fitted to match linear interaction analysis predictions journal, December 2010

Rayleigh-Taylor Instabilities of a Collapsing Cylindrical Shell in a Magnetic Field journal, January 1962

Computing multi-mode shock-induced compressible turbulent mixing at late times journal, August 2015

Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories journal, February 2000

Mathematical Modeling of Two-Phase Flow journal, January 1983

The mixing transition in RayleighTaylor instability journal, January 1999

Self-similarity and internal structure of turbulence induced by Rayleigh–Taylor instability journal, November 1999

Fluid dynamics in Group T-3 Los Alamos National Laboratory journal, April 2004

A k ‐ε model for turbulent mixing in shock‐tube flows induced by Rayleigh–Taylor instability journal, September 1990

Nonlinear Rayleigh-Taylor growth in converging geometry journal, May 2005

A hybrid-drive nonisobaric-ignition scheme for inertial confinement fusion journal, August 2016

Multimode seeded Richtmyer–Meshkov mixing in a convergent, compressible, miscible plasma system journal, May 2003

Numerical Simulations of Deep Nonlinear Richtymer‐Meshkov Instability journal, April 2000

Radiation driven planar foil instability and mix experiments at the AWE HELEN laser journal, January 1990

A study of ALE simulations of Rayleigh–Taylor instability journal, March 2001

Modeling hydrodynamic instabilities in inertial confinement fusion targets journal, December 2000

Measurement of Radiation-Driven Shock-Induced Mixing from Nonlinear Initial Perturbations journal, September 1995

Three-Dimensional Moving-Mesh Simulations of Galactic Center Cloud g2 journal, October 2012

A high-wavenumber viscosity for high-resolution numerical methods journal, April 2004

Numerical simulation of Richtmyer–Meshkov instabilities in shocked gas curtains journal, January 2011

Renormalization group theory for fluid and plasma turbulence journal, March 2010

A phenomenological treatment of rotating turbulence journal, August 1995

Statistical mechanics of simple coulomb systems journal, March 1980

Implosion of a spherical shock wave reflected from a spherical wall journal, January 1999

Suppression of Rayleigh–Taylor instability by the snowplow mechanism journal, April 1993

Suppression of Rayleigh-Taylor instabilities in Z-pinches journal, June 2015

Compressible Turbulent Mixing: Proceedings of the Fifth International Workshop conference, May 2017

Late-Time Mixing Sensitivity to Initial Broadband Surface Roughness in High-Energy-Density Shear Layers journal, November 2016

Density dependence of Rayleigh–Taylor and Richtmyer–Meshkov mixing fronts journal, April 2000

The Rayleigh–Taylor instability for inviscid and viscous fluids journal, March 2009

Onset of nonlinear saturation for Rayleigh-Taylor growth in the presence of a full spectrum of modes journal, June 1989

The magnetic Rayleigh–Taylor instability in astrophysical discs journal, July 2016

The prediction of laminarization with a two-equation model of turbulence journal, February 1972

Compressibility effects in Rayleigh–Taylor instability-induced flows journal, April 2010

Assessing Mix Layer Amplitude in 3D Decelerating Interface Experiments journal, December 2006

Comparison of two- and three-dimensional simulations of miscible Richtmyer-Meshkov instability with multimode initial conditions journal, October 2014

Small Atwood number Rayleigh–Taylor experiments journal, April 2010

Reactive Rayleigh-Taylor systems: Front propagation and non-stationarity journal, May 2011

The high-energy-density counterpropagating shear experiment and turbulent self-heating journal, December 2013

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

Extensible component-based architecture for FLASH, a massively parallel, multiphysics simulation code
journal, October 2009

Analysis of the effects of energy deposition on shock-driven turbulent mixing
journal, July 2013

A review of the ablative stabilization of the Rayleigh–Taylor instability in regimes relevant to inertial confinement fusion
journal, May 1994

Modal model for the nonlinear multimode Rayleigh–Taylor instability
journal, August 1996

Diagnostics hardening for harsh environment in Laser Mégajoule (invited)
journal, October 2008

High-Energy-Density Physics at the National Ignition Facility
journal, October 2017

The dynamics of shock accelerated light and heavy gas cylinders
journal, September 1993

Development of Richtmyer–Meshkov and Rayleigh–Taylor instability in the presence of magnetic field
journal, October 2011

Vorticity generation by shock propagation through bubbles in a gas
journal, April 1988

Dynamics of buoyancy-driven flows at moderately high Atwood numbers
journal, April 2016

Supernova mechanisms
journal, October 1990

On the identification of a vortex
journal, February 1995

Small amplitude theory of Richtmyer–Meshkov instability
journal, May 1994

The nonlinear large-eddy simulation method applied to Sc≈1 and Sc⪢1 passive-scalar mixing
journal, March 2008

Two-equation and multi-fluid turbulence models for Rayleigh–Taylor mixing
journal, December 2015

Anisotropy in turbulent flows and in turbulent transport
journal, July 2005

Dynamical evolution of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts
journal, September 2002

Initial conditions and modeling for simulations of shock driven turbulent material mixing
journal, June 2017

M IXING E FFICIENCY IN S TRATIFIED S HEAR F LOWS
journal, January 2003

Simulation ensemble for a laser–driven shear experiment
journal, September 2013

Richtmyer–Meshkov instability with strong radiatively driven shocks
journal, February 1996

Experimental study of Rayleigh–Taylor instability with a complex initial perturbation
journal, March 2009

Laser-driven compression of hollow shells: power requirements and stability limitations
journal, February 1976

Eddy damping, backscatter, and subgrid stresses in subgrid modeling of turbulence
journal, June 1991

On the control and suppression of the Rayleigh-Taylor instability using electric fields
journal, February 2014

The National Ignition Facility
journal, May 2001

First steps in modelling turbulence and its origins: a commentary on Reynolds (1895) ‘On the dynamical theory of incompressible viscous fluids and the determination of the criterion’
journal, April 2015

Rayleigh–Taylor instability of a continuously stratified fluid under a general rotation field
journal, July 1989

On hot-wire diagnostics in Rayleigh–Taylor mixing layers
journal, March 2009

Effect of shock proximity on Richtmyer–Meshkov growth
journal, May 2003

Rayleigh–Taylor instability in nonlinear Schrödinger flow
journal, July 2012

Spike morphology in blast-wave-driven instability experiments
journal, May 2010

The effects that changes in the diaphragm aperture have on the resulting shock tube flow
journal, April 2012

Spike Penetration in Blast-Wave-Driven Instabilities
journal, December 2011

Theory of the Rayleigh-Taylor instability
journal, August 1991

Effects of shear flow and transverse magnetic field on Richtmyer–Meshkov instability
journal, January 2008

A turbulent mixing Reynolds stress model fitted to match linear interaction analysis predictions
journal, December 2010

Rayleigh-Taylor Instabilities of a Collapsing Cylindrical Shell in a Magnetic Field
journal, January 1962

Computing multi-mode shock-induced compressible turbulent mixing at late times
journal, August 2015

Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories
journal, February 2000

Mathematical Modeling of Two-Phase Flow
journal, January 1983

The mixing transition in RayleighTaylor instability
journal, January 1999

Self-similarity and internal structure of turbulence induced by Rayleigh–Taylor instability
journal, November 1999

Fluid dynamics in Group T-3 Los Alamos National Laboratory
journal, April 2004

A k ‐ε model for turbulent mixing in shock‐tube flows induced by Rayleigh–Taylor instability
journal, September 1990

Nonlinear Rayleigh-Taylor growth in converging geometry
journal, May 2005

A hybrid-drive nonisobaric-ignition scheme for inertial confinement fusion
journal, August 2016

Multimode seeded Richtmyer–Meshkov mixing in a convergent, compressible, miscible plasma system
journal, May 2003

Numerical Simulations of Deep Nonlinear Richtymer‐Meshkov Instability
journal, April 2000

Radiation driven planar foil instability and mix experiments at the AWE HELEN laser
journal, January 1990

A study of ALE simulations of Rayleigh–Taylor instability
journal, March 2001

Modeling hydrodynamic instabilities in inertial confinement fusion targets
journal, December 2000

Measurement of Radiation-Driven Shock-Induced Mixing from Nonlinear Initial Perturbations
journal, September 1995

Three-Dimensional Moving-Mesh Simulations of Galactic Center Cloud g2
journal, October 2012

A high-wavenumber viscosity for high-resolution numerical methods
journal, April 2004

Numerical simulation of Richtmyer–Meshkov instabilities in shocked gas curtains
journal, January 2011

Renormalization group theory for fluid and plasma turbulence
journal, March 2010

A phenomenological treatment of rotating turbulence
journal, August 1995

Statistical mechanics of simple coulomb systems
journal, March 1980

Implosion of a spherical shock wave reflected from a spherical wall
journal, January 1999

Suppression of Rayleigh–Taylor instability by the snowplow mechanism
journal, April 1993

Suppression of Rayleigh-Taylor instabilities in Z-pinches
journal, June 2015

Compressible Turbulent Mixing: Proceedings of the Fifth International Workshop
conference, May 2017

Late-Time Mixing Sensitivity to Initial Broadband Surface Roughness in High-Energy-Density Shear Layers
journal, November 2016

Density dependence of Rayleigh–Taylor and Richtmyer–Meshkov mixing fronts
journal, April 2000

The Rayleigh–Taylor instability for inviscid and viscous fluids
journal, March 2009

Onset of nonlinear saturation for Rayleigh-Taylor growth in the presence of a full spectrum of modes
journal, June 1989

The magnetic Rayleigh–Taylor instability in astrophysical discs
journal, July 2016

The prediction of laminarization with a two-equation model of turbulence
journal, February 1972

Compressibility effects in Rayleigh–Taylor instability-induced flows
journal, April 2010

Assessing Mix Layer Amplitude in 3D Decelerating Interface Experiments
journal, December 2006

Comparison of two- and three-dimensional simulations of miscible Richtmyer-Meshkov instability with multimode initial conditions
journal, October 2014

Small Atwood number Rayleigh–Taylor experiments
journal, April 2010

Reactive Rayleigh-Taylor systems: Front propagation and non-stationarity
journal, May 2011

The high-energy-density counterpropagating shear experiment and turbulent self-heating
journal, December 2013

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

Verification of compressible closure models for turbulent multifluid mixing
journal, February 2017

Experiments on the late-time development of single-mode Richtmyer–Meshkov instability
journal, March 2005

Influence of initial conditions on the flow patterns of a shock‐accelerated thin fluid layer
journal, November 1994

The Rayleigh–Taylor instability and internal waves in quantum plasmas
journal, April 2008