# Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation

## Abstract

High-fidelity large eddy simulation (LES) of a low-Atwood number (A = 0.05) Rayleigh-Taylor mixing layer is performed using the tenth-order compact difference code Miranda. An initial multimode perturbation spectrum is specified in Fourier space as a function of mesh resolution such that a database of results is obtained in which each successive level of increased grid resolution corresponds approximately to one additional doubling of the mixing layer width, or generation. The database is then analyzed to determine approximate requirements for self-similarity, and a new metric is proposed to quantify how far a given simulation is from the limit of self-similarity. It is determined that mixing layer growth reaches a high degree of self-similarity after approximately 4.5 generations. Statistical convergence errors and boundary effects at late time, however, make it impossible to draw similar conclusions regarding the self-similar growth of more sensitive turbulence parameters. Finally, self-similar turbulence profiles from the LES database are compared with one-dimensional simulations using the k-L-a and BHR-2 Reynolds-averaged Navier-Stokes (RANS) models. The k-L-a model, which is calibrated to reproduce a quadratic turbulence kinetic energy profile for a self-similar mixing layer, is found to be in better agreement with the LES than BHR-2 results.

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Univ. of Missouri, Columbia, MO (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1430929

- Report Number(s):
- LLNL-JRNL-681041

Journal ID: ISSN 1468-5248

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Turbulence (Online)

- Additional Journal Information:
- Journal Name: Journal of Turbulence (Online); Journal Volume: 18; Journal Issue: 10; Journal ID: ISSN 1468-5248

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; 70 PLASMA PHYSICS AND FUSION

### Citation Formats

```
Morgan, B. E., Olson, B. J., White, J. E., and McFarland, J. A. Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation. United States: N. p., 2017.
Web. doi:10.1080/14685248.2017.1343477.
```

```
Morgan, B. E., Olson, B. J., White, J. E., & McFarland, J. A. Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation. United States. doi:10.1080/14685248.2017.1343477.
```

```
Morgan, B. E., Olson, B. J., White, J. E., and McFarland, J. A. Thu .
"Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation". United States. doi:10.1080/14685248.2017.1343477. https://www.osti.gov/servlets/purl/1430929.
```

```
@article{osti_1430929,
```

title = {Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation},

author = {Morgan, B. E. and Olson, B. J. and White, J. E. and McFarland, J. A.},

abstractNote = {High-fidelity large eddy simulation (LES) of a low-Atwood number (A = 0.05) Rayleigh-Taylor mixing layer is performed using the tenth-order compact difference code Miranda. An initial multimode perturbation spectrum is specified in Fourier space as a function of mesh resolution such that a database of results is obtained in which each successive level of increased grid resolution corresponds approximately to one additional doubling of the mixing layer width, or generation. The database is then analyzed to determine approximate requirements for self-similarity, and a new metric is proposed to quantify how far a given simulation is from the limit of self-similarity. It is determined that mixing layer growth reaches a high degree of self-similarity after approximately 4.5 generations. Statistical convergence errors and boundary effects at late time, however, make it impossible to draw similar conclusions regarding the self-similar growth of more sensitive turbulence parameters. Finally, self-similar turbulence profiles from the LES database are compared with one-dimensional simulations using the k-L-a and BHR-2 Reynolds-averaged Navier-Stokes (RANS) models. The k-L-a model, which is calibrated to reproduce a quadratic turbulence kinetic energy profile for a self-similar mixing layer, is found to be in better agreement with the LES than BHR-2 results.},

doi = {10.1080/14685248.2017.1343477},

journal = {Journal of Turbulence (Online)},

number = 10,

volume = 18,

place = {United States},

year = {2017},

month = {6}

}

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Works referenced in this record:

##
The mixing transition in turbulent flows

journal, April 2000

- Dimotakis, Paul E.
- Journal of Fluid Mechanics, Vol. 409

##
Large and Small Scale Structure in Rayleigh-Taylor Mixing

journal, April 1998

- Schneider, Marilyn B.; Dimonte, Guy; Remington, Bruce
- Physical Review Letters, Vol. 80, Issue 16

##
Development and validation of a turbulent-mix model for variable-density and compressible flows

journal, October 2010

- Banerjee, Arindam; Gore, Robert A.; Andrews, Malcolm J.
- Physical Review E, Vol. 82, Issue 4

##
Analysis of turbulent transport and mixing in transitional Rayleigh–Taylor unstable flow using direct numerical simulation data

journal, October 2010

- Schilling, Oleg; Mueschke, Nicholas J.
- Physics of Fluids, Vol. 22, Issue 10

##
Measurements of molecular mixing in a high-Schmidt-number Rayleigh–Taylor mixing layer

journal, July 2009

- Mueschke, Nicholas J.; Schilling, Oleg; Youngs, David L.
- Journal of Fluid Mechanics, Vol. 632

##
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

##
The Role of Mixing in Astrophysics

journal, April 2000

- Arnett, D.
- The Astrophysical Journal Supplement Series, Vol. 127, Issue 2

##
The dynamics of the *k* –ϵ mix model toward its self-similar Rayleigh–Taylor solution

journal, November 2014

- Gréa, Benoît-Joseph
- Journal of Turbulence, Vol. 16, Issue 2

##
Two-equation and multi-fluid turbulence models for Rayleigh–Taylor mixing

journal, December 2015

- Kokkinakis, I. W.; Drikakis, D.; Youngs, D. L.
- International Journal of Heat and Fluid Flow, Vol. 56

##
Investigation of Rayleigh–Taylor turbulence and mixing using direct numerical simulation with experimentally measured initial conditions. I. Comparison to experimental data

journal, January 2009

- Mueschke, Nicholas J.; Schilling, Oleg
- Physics of Fluids, Vol. 21, Issue 1

##
Nonlinear effects in the combined Rayleigh-Taylor/Kelvin-Helmholtz instability

journal, November 2011

- Olson, Britton J.; Larsson, Johan; Lele, Sanjiva K.
- Physics of Fluids, Vol. 23, Issue 11

##
Investigation of Rayleigh–Taylor turbulence and mixing using direct numerical simulation with experimentally measured initial conditions. II. Dynamics of transitional flow and mixing statistics

journal, January 2009

- Mueschke, Nicholas J.; Schilling, Oleg
- Physics of Fluids, Vol. 21, Issue 1

##
Experimental study of Rayleigh–Taylor instability with a complex initial perturbation

journal, March 2009

- Olson, D. H.; Jacobs, J. W.
- Physics of Fluids, Vol. 21, Issue 3

##
Artificial fluid properties for large-eddy simulation of compressible turbulent mixing

journal, May 2007

- Cook, Andrew W.
- Physics of Fluids, Vol. 19, Issue 5

##
Large-eddy and unsteady RANS simulations of a shock-accelerated heavy gas cylinder

journal, April 2015

- Morgan, B. E.; Greenough, J. A.
- Shock Waves, Vol. 26, Issue 4

##
Detailed measurements of a statistically steady Rayleigh–Taylor mixing layer from small to high Atwood numbers

journal, August 2010

- Banerjee, Arindam; Kraft, Wayne N.; Andrews, Malcolm J.
- Journal of Fluid Mechanics, Vol. 659

##
Progress toward Ignition and Burn Propagation in Inertial Confinement Fusion

journal, September 1992

- Lindl, John D.; McCrory, Robert L.; Campbell, E. Michael
- Physics Today, Vol. 45, Issue 9

##
K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities

journal, August 2006

- Dimonte, Guy; Tipton, Robert
- Physics of Fluids, Vol. 18, Issue 8

##
The Tilted Rocket Rig: A Rayleigh–Taylor Test Case for RANS Models1

journal, July 2014

- Denissen, Nicholas A.; Rollin, Bertrand; Reisner, Jon M.
- Journal of Fluids Engineering, Vol. 136, Issue 9

##
Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meskov instabilities

journal, April 2015

- Morgan, Brandon E.; Wickett, Michael E.
- Physical Review E, Vol. 91, Issue 4

##
Large eddy simulation requirements for the Richtmyer-Meshkov instability

journal, April 2014

- Olson, Britton J.; Greenough, Jeff
- Physics of Fluids, Vol. 26, Issue 4

##
On generating initial conditions for turbulence models: the case of Rayleigh–Taylor instability turbulent mixing

journal, March 2013

- Rollin, B.; Andrews, M. J.
- Journal of Turbulence, Vol. 14, Issue 3

##
Numerical simulation of turbulent mixing by Rayleigh-Taylor instability

journal, July 1984

- Youngs, David L.
- Physica D: Nonlinear Phenomena, Vol. 12, Issue 1-3

##
New phenomena in variable-density Rayleigh–Taylor turbulence

journal, December 2010

- Livescu, D.; Ristorcelli, J. R.; Petersen, M. R.
- Physica Scripta, Vol. T142

##
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

##
Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells

journal, September 1990

- Mikaelian, Karnig O.
- Physical Review A, Vol. 42, Issue 6

##
An overview of Rayleigh-Taylor instability

journal, July 1984

- Sharp, D. H.
- Physica D: Nonlinear Phenomena, Vol. 12, Issue 1-3

##
The mixing transition in RayleighTaylor instability

journal, January 1999

- Cook, Andrew W.; Cabot, William; Miller, Paul L.
- Journal of Fluid Mechanics, Vol. 511

##
Self-similarity and internal structure of turbulence induced by Rayleigh–Taylor instability

journal, November 1999

- Dalziel, S. B.; Linden, P. F.; Youngs, D. L.
- Journal of Fluid Mechanics, Vol. 399

##
Inertial-range anisotropy in Rayleigh-Taylor turbulence

journal, February 2012

- Soulard, Olivier; Griffond, Jérôme
- Physics of Fluids, Vol. 24, Issue 2

##
Effect of shear on Rayleigh-Taylor mixing at small Atwood number

journal, March 2013

- Akula, Bhanesh; Andrews, Malcolm J.; Ranjan, Devesh
- Physical Review E, Vol. 87, Issue 3

##
Modelling turbulent mixing by Rayleigh-Taylor instability

journal, July 1989

- Youngs, David L.
- Physica D: Nonlinear Phenomena, Vol. 37, Issue 1-3

##
The rapid acceleration model and the growth rate of a turbulent mixing zone induced by Rayleigh-Taylor instability

journal, January 2013

- Gréa, B. -J.
- Physics of Fluids, Vol. 25, Issue 1

##
Dynamics and structure of unstably stratified homogeneous turbulence

journal, June 2016

- Gréa, Benoît-Joseph; Burlot, Alan; Godeferd, Fabien
- Journal of Turbulence, Vol. 17, Issue 7

##
Modal interactions between a large-wavelength inclined interface and small-wavelength multimode perturbations in a Richtmyer-Meshkov instability

journal, July 2015

- McFarland, Jacob A.; Reilly, David; Black, Wolfgang
- Physical Review E, Vol. 92, Issue 1

##
Rayleigh–Taylor turbulence: self-similar analysis and direct numerical simulations

journal, May 2004

- Ristorcelli, J. R.; Clark, T. T.
- Journal of Fluid Mechanics, Vol. 507

##
A comparative study of the turbulent Rayleigh–Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration

journal, May 2004

- Dimonte, Guy; Youngs, D. L.; Dimits, A.
- Physics of Fluids, Vol. 16, Issue 5

##
Enthalpy diffusion in multicomponent flows

journal, May 2009

- Cook, Andrew W.
- Physics of Fluids, Vol. 21, Issue 5

##
Rayleigh–Taylor instability in complex stratifications

journal, October 2005

- Jacobs, J. W.; Dalziel, S. B.
- Journal of Fluid Mechanics, Vol. 542, Issue -1

##
The role of directionality on the structure and dynamics of strongly anisotropic turbulent flows

journal, January 2013

- Cambon, C.; Gréa, B. -J.
- Journal of Turbulence, Vol. 14, Issue 1

##
Applications of shock-induced mixing to supersonic combustion

journal, May 1993

- Yang, Joseph; Kubota, Toshi; Zukoski, Edward E.
- AIAA Journal, Vol. 31, Issue 5

##
Self-similarity and universality in Rayleigh–Taylor, Boussinesq turbulence

journal, January 2009

- Vladimirova, Natalia; Chertkov, Michael
- Physics of Fluids, Vol. 21, Issue 1

##
Bubble merger model for the nonlinear Rayleigh–Taylor instability driven by a strong blast wave

journal, November 2004

- Miles, A. R.
- Physics of Plasmas, Vol. 11, Issue 11

##
Experimental investigation of RayleighTaylor mixing at small Atwood numbers

journal, January 1999

- Ramaprabhu, P.; Andrews, M. J.
- Journal of Fluid Mechanics, Vol. 502

##
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

##
Statistics of mixing in three-dimensional Rayleigh–Taylor turbulence at low Atwood number and Prandtl number one

journal, March 2010

- Boffetta, G.; Mazzino, A.; Musacchio, S.
- Physics of Fluids, Vol. 22, Issue 3

##
Rayleigh–Taylor shock waves

journal, December 2007

- Olson, Britton J.; Cook, Andrew W.
- Physics of Fluids, Vol. 19, Issue 12

##
Comparison of two- and three-dimensional simulations of miscible Richtmyer-Meshkov instability with multimode initial conditions

journal, October 2014

- Olson, Britton J.; Greenough, Jeffrey A.
- Physics of Fluids, Vol. 26, Issue 10

##
Experimental characterization of initial conditions and spatio-temporal evolution of a small-Atwood-number Rayleigh–Taylor mixing layer

journal, October 2006

- Mueschke, Nicholas J.; Andrews, Malcolm J.; Schilling, Oleg
- Journal of Fluid Mechanics, Vol. 567

##
A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing

journal, September 2015

- Schwarzkopf, J. D.; Livescu, D.; Baltzer, J. R.
- Flow, Turbulence and Combustion, Vol. 96, Issue 1

##
Impact of domain size and statistical errors in simulations of homogeneous decaying turbulence and the Richtmyer-Meshkov instability

journal, April 2016

- Thornber, B.
- Physics of Fluids, Vol. 28, Issue 4

##
Transition stages of Rayleigh–Taylor instability between miscible fluids

journal, September 2001

- Cook, Andrew W.; Dimotakis, Paul E.
- Journal of Fluid Mechanics, Vol. 443