Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: The effect of initial conditions on mixing transition of the Richtmyer–Meshkov instability

Abstract

We investigate the late-time Richtmyer–Meshkov instability (RMI) growth of sinuous perturbations on an air/sulphur hexafluoride interface (Atwood number, A ~ 0.67 ) subjected to a Mach 1.2 planar shock wave at Los Alamos National Laboratory's vertical shock tube facility. Interface perturbations are established using a novel membraneless technique where cross-flowing air and SF6 separated by an oscillating splitter plate create a perturbed density interface. The interface formed has multi-modal features and residual small perturbations, however, a dominant mode is still noticeable. The late-time perturbation growths scale with $$ka_0$$ initial conditions (where $$k$$ is the wavenumber and $$a_0$$ is the initial amplitude of the dominant mode) as measured at the pre-shock interface. Past nonlinear models based on potential-flow theory, heuristic/interpolation approaches, Padé approximants and numerical simulations are evaluated against present experimental results. Accounting for an explicit $$ka_0$$ dependence in Sadot et al.'s model, we propose an empirical rational function that captures the asymptotic behaviour of perturbation growth for a broad range of initial conditions ( 0.30 $$≤ ka_0 ≤$$ 0.86 ). The onset of mixing transition and its initial condition dependence are investigated with respect to the minimum state criterion ($Re =$ 1.6 $$\times$$ 105 ) for unsteady flows by Zhou. Earlier mixing transitions for higher ka0 initial conditions are noted from local and global Reynolds number estimates which are corroborated by the existence of an inertial sub-range and formation of mixing regions indicating the physical significance of the minimum state criterion in RMI flows. The transition is accompanied by the increasing teapot-like appearance of joint probability density functions of $p–q$ (invariants of the reduced velocity gradient tensor), establishing the technique as a useful tool for turbulence detection in two-dimensional diagnostics.

Authors:
ORCiD logo [1];  [1];  [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]
+ Show Author Affiliations
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1688756
Report Number(s):
LA-UR-19-31658
Journal ID: ISSN 0022-1120; TRN: US2204135
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Fluid Mechanics
Additional Journal Information:
Journal Volume: 904; Journal ID: ISSN 0022-1120
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Richtmyer-Meshkov instability; transition to turbulence; baroclinic flows; vortex dynamics

Citation Formats

Mansoor, Mohammad Mujtaba, Dalton, Sean Michael, Martinez, Adam Andrew, Desjardins, Tiffany, Charonko, John James, and Prestridge, Katherine Philomena. The effect of initial conditions on mixing transition of the Richtmyer–Meshkov instability. United States: N. p., 2020. Web. doi:10.1017/jfm.2020.620.
Copy to clipboard
Mansoor, Mohammad Mujtaba, Dalton, Sean Michael, Martinez, Adam Andrew, Desjardins, Tiffany, Charonko, John James, & Prestridge, Katherine Philomena. The effect of initial conditions on mixing transition of the Richtmyer–Meshkov instability. United States. https://doi.org/10.1017/jfm.2020.620
Copy to clipboard
Mansoor, Mohammad Mujtaba, Dalton, Sean Michael, Martinez, Adam Andrew, Desjardins, Tiffany, Charonko, John James, and Prestridge, Katherine Philomena. Mon . "The effect of initial conditions on mixing transition of the Richtmyer–Meshkov instability". United States. https://doi.org/10.1017/jfm.2020.620. https://www.osti.gov/servlets/purl/1688756.
Copy to clipboard
@article{osti_1688756,
title = {The effect of initial conditions on mixing transition of the Richtmyer–Meshkov instability},
author = {Mansoor, Mohammad Mujtaba and Dalton, Sean Michael and Martinez, Adam Andrew and Desjardins, Tiffany and Charonko, John James and Prestridge, Katherine Philomena},
abstractNote = {We investigate the late-time Richtmyer–Meshkov instability (RMI) growth of sinuous perturbations on an air/sulphur hexafluoride interface (Atwood number, A ~ 0.67 ) subjected to a Mach 1.2 planar shock wave at Los Alamos National Laboratory's vertical shock tube facility. Interface perturbations are established using a novel membraneless technique where cross-flowing air and SF6 separated by an oscillating splitter plate create a perturbed density interface. The interface formed has multi-modal features and residual small perturbations, however, a dominant mode is still noticeable. The late-time perturbation growths scale with $ka_0$ initial conditions (where $k$ is the wavenumber and $a_0$ is the initial amplitude of the dominant mode) as measured at the pre-shock interface. Past nonlinear models based on potential-flow theory, heuristic/interpolation approaches, Padé approximants and numerical simulations are evaluated against present experimental results. Accounting for an explicit $ka_0$ dependence in Sadot et al.'s model, we propose an empirical rational function that captures the asymptotic behaviour of perturbation growth for a broad range of initial conditions ( 0.30 $≤ ka_0 ≤$ 0.86 ). The onset of mixing transition and its initial condition dependence are investigated with respect to the minimum state criterion ($Re =$ 1.6 $\times$ 105 ) for unsteady flows by Zhou. Earlier mixing transitions for higher ka0 initial conditions are noted from local and global Reynolds number estimates which are corroborated by the existence of an inertial sub-range and formation of mixing regions indicating the physical significance of the minimum state criterion in RMI flows. The transition is accompanied by the increasing teapot-like appearance of joint probability density functions of $p–q$ (invariants of the reduced velocity gradient tensor), establishing the technique as a useful tool for turbulence detection in two-dimensional diagnostics.},
doi = {10.1017/jfm.2020.620},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 904,
place = {United States},
year = {Mon Oct 05 00:00:00 EDT 2020},
month = {Mon Oct 05 00:00:00 EDT 2020}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1017/jfm.2020.620
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Turbulent Inflow Conditions for Large-Eddy-Simulation of Compressible Wall-Bounded Flows
journal, March 2004

  • Sagaut, Pierre; Garnier, Eric; Tromeur, Eric
  • AIAA Journal, Vol. 42, Issue 3
  • DOI: 10.2514/1.3461

The mixing transition in turbulent flows
journal, April 2000

Bubble competition in Rayleigh–Taylor instability
journal, January 1988

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

  • Jacobs, J. W.; Krivets, V. V.
  • Physics of Fluids, Vol. 17, Issue 3
  • DOI: 10.1063/1.1852574

A First Course in Turbulence
January 1972

Turbulent mixing measurements in the Richtmyer-Meshkov instability
journal, July 2012

  • Weber, Christopher; Haehn, Nicholas; Oakley, Jason
  • Physics of Fluids, Vol. 24, Issue 7
  • DOI: 10.1063/1.4733447

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

  • Budzinski, John M.; Benjamin, Robert F.; Jacobs, Jeffrey W.
  • Physics of Fluids, Vol. 6, Issue 11
  • DOI: 10.1063/1.868447

A membraneless experiment for the study of Richtmyer–Meshkov instability of a shock-accelerated gas interface
journal, October 1997

  • Jones, M. A.; Jacobs, J. W.
  • Physics of Fluids, Vol. 9, Issue 10
  • DOI: 10.1063/1.869416

An experimental investigation of the turbulent mixing transition in the Richtmyer–Meshkov instability
journal, May 2014

  • Weber, Christopher R.; Haehn, Nicholas S.; Oakley, Jason G.
  • Journal of Fluid Mechanics, Vol. 748
  • DOI: 10.1017/jfm.2014.188

Vortex Identification Methodology for Feed Insertion Guidance in Fluid Mixing Processes
journal, January 2007

  • Ducci, A.; Yianneskis, M.
  • Chemical Engineering Research and Design, Vol. 85, Issue 5
  • DOI: 10.1205/cherd06192

Turbulent mixing induced by Richtmyer-Meshkov instability
conference, January 2017

  • Krivets, V. V.; Ferguson, K. J.; Jacobs, J. W.
  • SHOCK COMPRESSION OF CONDENSED MATTER - 2015: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, AIP Conference Proceedings
  • DOI: 10.1063/1.4971732

Turbulent mixing generated by Rayleigh-Taylor and Richtmyer-Meshkov instabilities
journal, August 1989

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

A numerical study of bubble interactions in Rayleigh–Taylor instability for compressible fluids
journal, November 1990

  • Glimm, J.; Li, X. L.; Menikoff, R.
  • Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 11
  • DOI: 10.1063/1.857679

Turbulent Richtmyer–Meshkov instability experiments with strong radiatively driven shocks
journal, December 1997

  • Dimonte, Guy; Schneider, Marilyn
  • Physics of Plasmas, Vol. 4, Issue 12
  • DOI: 10.1063/1.872597

Scaling evolution in shock-induced transition to turbulence
journal, December 2003

On the identification of a vortex
journal, February 1995

Analytic Approach to Nonlinear Rayleigh-Taylor and Richtmyer-Meshkov Instabilities
journal, January 1998

Digital particle image velocimetry (DPIV) robust phase correlation
journal, April 2009

An elaborate experiment on the single-mode Richtmyer–Meshkov instability
journal, August 2018

Intermittency and cascades
journal, April 2000

Density gradient stabilization of the Richtmyer–Meshkov instability
journal, November 1991

  • Mikaelian, Karnig O.
  • Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 11
  • DOI: 10.1063/1.858152

Comparison of vortex identification criteria for planar velocity fields in wall turbulence
journal, August 2015

  • Chen, Qigang; Zhong, Qiang; Qi, Meilan
  • Physics of Fluids, Vol. 27, Issue 8
  • DOI: 10.1063/1.4927647

Vortex-accelerated secondary baroclinic vorticity deposition and late-intermediate time dynamics of a two-dimensional Richtmyer–Meshkov interface
journal, December 2003

  • Peng, Gaozhu; Zabusky, Norman J.; Zhang, Shuang
  • Physics of Fluids, Vol. 15, Issue 12
  • DOI: 10.1063/1.1621628

Evaluation of turbulent mixing transition in a shock-driven variable-density flow
journal, October 2017

  • Mohaghar, Mohammad; Carter, John; Musci, Benjamin
  • Journal of Fluid Mechanics, Vol. 831
  • DOI: 10.1017/jfm.2017.664

An experimental and numerical investigation of the dependency on the initial conditions of the Richtmyer-Meshkov instability
journal, February 2014

  • Vandenboomgaerde, Marc; Souffland, Denis; Mariani, Christian
  • Physics of Fluids, Vol. 26, Issue 2
  • DOI: 10.1063/1.4865836

The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability
journal, May 2010

Potential flow models of Rayleigh–Taylor and Richtmyer–Meshkov bubble fronts
journal, December 1994

  • Hecht, Jacob; Alon, Uri; Shvarts, Dov
  • Physics of Fluids, Vol. 6, Issue 12
  • DOI: 10.1063/1.868391

Turbulent Flows
book, July 2012

Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory
journal, February 2016

  • Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.
  • Journal of Fluid Mechanics, Vol. 791
  • DOI: 10.1017/jfm.2016.46

On the Richtmyer–Meshkov instability evolving from a deterministic multimode planar interface
journal, August 2014

  • Tritschler, V. K.; Olson, B. J.; Lele, S. K.
  • Journal of Fluid Mechanics, Vol. 755
  • DOI: 10.1017/jfm.2014.436

Experimental study of the Richtmyer-Meshkov instability induced by a Mach 3 shock wave
journal, June 2004

Weakly nonlinear hydrodynamic instabilities in inertial fusion
journal, August 1991

  • Haan, S. W.
  • Physics of Fluids B: Plasma Physics, Vol. 3, Issue 8
  • DOI: 10.1063/1.859603

Turbulent mixing in a Richtmyer–Meshkov fluid layer after reshock: velocity and density statistics
journal, March 2012

  • Balakumar, B. J.; Orlicz, G. C.; Ristorcelli, J. R.
  • Journal of Fluid Mechanics, Vol. 696
  • DOI: 10.1017/jfm.2012.8

Nonlinear theory of unstable fluid mixing driven by shock wave
journal, April 1997

  • Zhang, Qiang; Sohn, Sung-Ik
  • Physics of Fluids, Vol. 9, Issue 4
  • DOI: 10.1063/1.869202

Numerical simulation of turbulent mixing by Rayleigh-Taylor instability
journal, July 1984

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

  • Dimonte, Guy; Schneider, Marilyn
  • Physics of Fluids, Vol. 12, Issue 2
  • DOI: 10.1063/1.870309

Design of a fast diaphragmless shock tube driver
journal, July 2015

Physics of the single-shocked and reshocked Richtmyer–Meshkov instability
journal, January 2012

Three-dimensional simulation of a Richtmyer–Meshkov instability with a two-scale initial perturbation
journal, October 2002

  • Cohen, Ronald H.; Dannevik, William P.; Dimits, Andris M.
  • Physics of Fluids, Vol. 14, Issue 10
  • DOI: 10.1063/1.1504452

An overview of Rayleigh-Taylor instability
journal, July 1984

Experiments on the Richtmyer–Meshkov instability: single-scale perturbations on a continuous interface
journal, March 1994

Experimental observations of the mixing transition in a shock-accelerated gas curtain
journal, January 1999

  • Rightley, P. M.; Vorobieff, P.; Martin, R.
  • Physics of Fluids, Vol. 11, Issue 1
  • DOI: 10.1063/1.869911

A linear electric motor to study turbulent hydrodynamics
journal, January 1996

  • Dimonte, Guy; Morrison, Jim; Hulsey, Scott
  • Review of Scientific Instruments, Vol. 67, Issue 1
  • DOI: 10.1063/1.1146585

Mixing transition in a shocked variable-density flow
journal, November 2015

  • Orlicz, G. C.; Balasubramanian, Sridhar; Vorobieff, P.
  • Physics of Fluids, Vol. 27, Issue 11
  • DOI: 10.1063/1.4935183

A general classification of three‐dimensional flow fields
journal, May 1990

  • Chong, M. S.; Perry, A. E.; Cantwell, B. J.
  • Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 5
  • DOI: 10.1063/1.857730

Transition to turbulence in shock-driven mixing: a Mach number study
journal, November 2011

  • Lombardini, M.; Pullin, D. I.; Meiron, D. I.
  • Journal of Fluid Mechanics, Vol. 690
  • DOI: 10.1017/jfm.2011.425

Experimental study of the Richtmyer–Meshkov instability of incompressible fluids
journal, May 2003

Incident shock Mach number effects on Richtmyer-Meshkov mixing in a heavy gas layer
journal, November 2013

  • Orlicz, G. C.; Balasubramanian, S.; Prestridge, K. P.
  • Physics of Fluids, Vol. 25, Issue 11
  • DOI: 10.1063/1.4827435

PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/SF 6 interface
journal, August 2002

Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence
journal, October 2013

  • Tomkins, C. D.; Balakumar, B. J.; Orlicz, G.
  • Journal of Fluid Mechanics, Vol. 735
  • DOI: 10.1017/jfm.2013.430

Simulations and model of the nonlinear Richtmyer–Meshkov instability
journal, January 2010

  • Dimonte, Guy; Ramaprabhu, P.
  • Physics of Fluids, Vol. 22, Issue 1
  • DOI: 10.1063/1.3276269

Richtmyer-Meshkov instability of a flat interface subjected to a rippled shock wave
journal, January 2017

Experiments on the Richtmyer–Meshkov instability with an imposed, random initial perturbation
journal, March 2013

X‐ray measurements of growth rates at a gas interface accelerated by shock waves
journal, September 1996

  • Bonazza, R.; Sturtevant, B.
  • Physics of Fluids, Vol. 8, Issue 9
  • DOI: 10.1063/1.869033

Vortex simulations of the Rayleigh–Taylor instability
journal, January 1980

  • Baker, Gregory R.; Meiron, Daniel I.; Orszag, Steven A.
  • Physics of Fluids, Vol. 23, Issue 8
  • DOI: 10.1063/1.863173

Invariants of the reduced velocity gradient tensor in turbulent flows
journal, January 2013

  • Cardesa, J. I.; Mistry, D.; Gan, L.
  • Journal of Fluid Mechanics, Vol. 716
  • DOI: 10.1017/jfm.2012.558

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

Padé approximation to an interfacial fluid mixing problem
journal, September 1997

Mechanisms for generating coherent packets of hairpin vortices in channel flow
journal, May 1999

Instability growth patterns of a shock-accelerated thin fluid layer
journal, February 1993

A new vertical shock tube for Rayleigh-Taylor instability measurements
conference, January 1990

  • Cavailler, C.; Mercier, P.; Rodriguez, G.
  • Current topics in shock waves 17th international symposium on shock waves and shock tubes Bethlehem, Pennsylvania (USA), AIP Conference Proceedings
  • DOI: 10.1063/1.39391

The late-time development of the Richtmyer–Meshkov instability
journal, August 2000

  • Prasad, J. K.; Rasheed, A.; Kumar, S.
  • Physics of Fluids, Vol. 12, Issue 8
  • DOI: 10.1063/1.870456

Onset of turbulence in accelerated high-Reynolds-number flow
journal, May 2003

High-Amplitude Single-Mode Perturbation Evolution at the Richtmyer-Meshkov Instability
journal, November 2005

Instability of the interface of two gases accelerated by a shock wave
journal, January 1972

On shock polar analysis and analytical expressions for vorticity deposition in shock‐accelerated density‐stratified interfaces
journal, June 1993

  • Samtaney, Ravi; Zabusky, Norman J.
  • Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 6
  • DOI: 10.1063/1.858618

Simultaneous density-field visualization and PIV of a shock-accelerated gas curtain
journal, October 2000

  • Prestridge, K.; Rightley, P. M.; Vorobieff, P.
  • Experiments in Fluids, Vol. 29, Issue 4
  • DOI: 10.1007/s003489900091

Study of Nonlinear Evolution of Single-Mode and Two-Bubble Interaction under Richtmyer-Meshkov Instability
journal, February 1998

The time scale for the transition to turbulence in a high Reynolds number, accelerated flow
journal, March 2003

  • Robey, H. F.; Zhou, Ye; Buckingham, A. C.
  • Physics of Plasmas, Vol. 10, Issue 3
  • DOI: 10.1063/1.1534584

Taylor instability in shock acceleration of compressible fluids
journal, May 1960

  • Richtmyer, Robert D.
  • Communications on Pure and Applied Mathematics, Vol. 13, Issue 2
  • DOI: 10.1002/cpa.3160130207

Simulations of Richtmyer–Meshkov instabilities in planar shock-tube experiments
journal, March 2011

  • Grinstein, F. F.; Gowardhan, A. A.; Wachtor, A. J.
  • Physics of Fluids, Vol. 23, Issue 3
  • DOI: 10.1063/1.3555635

Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock
journal, June 2006

Progress in understanding turbulent mixing induced by Rayleigh–Taylor and Richtmyer–Meshkov instabilities
journal, May 2003

  • Zhou, Ye; Remington, B. A.; Robey, H. F.
  • Physics of Plasmas, Vol. 10, Issue 5
  • DOI: 10.1063/1.1560923

Experimental Study for ICF-Related Richtmyer-Meshkov Instabilities
journal, November 2007

  • Motl, B. J.; Niederhaus, J. H. J.; Ranjan, D.
  • Fusion Science and Technology, Vol. 52, Issue 4
  • DOI: 10.13182/FST07-A1640

Investigation of the Richtmyer-Meshkov Instability with Stereolithographed Interfaces
journal, June 2008

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

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

On the late-time growth of the two-dimensional Richtmyer–Meshkov instability in shock tube experiments
journal, October 2012

  • Morgan, Robert V.; Aure, R.; Stockero, J. D.
  • Journal of Fluid Mechanics, Vol. 712
  • DOI: 10.1017/jfm.2012.426

Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part 2. The fine structure
journal, March 1981

The effects of initial conditions and circulation deposition on the inclined-interface reshocked Richtmyer–Meshkov instability
journal, August 2015

    Sort by:
    [ × clear filter / sort ]

    Similar Records in DOE PAGES and OSTI.GOV collections: