# Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ-group collaboration

## Abstract

Turbulent Richtmyer–Meshkov instability (RMI) is investigated through a series of high resolution three-dimensional simulations of two initial conditions with eight independent codes. The simulations are initialised with a narrowband perturbation such that instability growth is due to non-linear coupling/backscatter from the energetic modes, thus generating the lowest expected growth rate from a pure RMI. By independently assessing the results from each algorithm and computing ensemble averages of multiple algorithms, the results allow a quantification of key flow properties as well as the uncertainty due to differing numerical approaches. A new analytical model predicting the initial layer growth for a multimode narrowband perturbation is presented, along with two models for the linear and non-linear regimes combined. Overall, the growth rate exponent is determined as θ=0.292±0.009, in good agreement with prior studies; however, the exponent is decaying slowly in time. Also, θ is shown to be relatively insensitive to the choice of mixing layer width measurements. The asymptotic integral molecular mixing measures Θ=0.792±0.014, Ξ=0.800±0.014, and Ψ=0.782±0.013 are lower than some experimental measurements but within the range of prior numerical studies. The flow field is shown to be persistently anisotropic for all algorithms, at the latest time having between 49% and 66% highermore »

- Authors:

- Univ. of Sydney, NSW (Australia). School of Aerospace, Mechanical and Mechatronic Engineering
- Alternative Energies and Atomic Energy Commission (CEA), Arpajon (France)
- Univ. of North Carolina, Charlotte, NC (United States). Mechanical Engineering and Engineering Science
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- AWE, Aldermaston (United Kingdom)
- Russian Academy of Sciences (RAS), Moscow (Russian Federation). Keldysh Inst. of Applied Mathematics; Russian Academy of Sciences (RAS), Moscow (Russian Federation). P.N. Lebedev Physical Inst.
- Russian Academy of Sciences (RAS), Moscow (Russian Federation). Keldysh Inst. of Applied Mathematics
- Russian Academy of Sciences (RAS), Moscow (Russian Federation). P.N. Lebedev Physical Inst.
- Univ. of Strathclyde, Glasgow (Scotland). Dept. of Mechanical and Aerospace Engineering

- Publication Date:

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

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

- OSTI Identifier:
- 1468910

- Alternate Identifier(s):
- OSTI ID: 1402116

- Report Number(s):
- LLNL-JRNL-733858

Journal ID: ISSN 1070-6631; 885603

- Grant/Contract Number:
- AC52-07NA27344; AC52-07NA2734; AC52-06NA2-5396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics of Fluids

- Additional Journal Information:
- Journal Volume: 29; Journal Issue: 10; Journal ID: ISSN 1070-6631

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Thornber, B., Griffond, J., Poujade, O., Attal, N., Varshochi, H., Bigdelou, P., Ramaprabhu, P., Olson, B., Greenough, J., Zhou, Y., Schilling, O., Garside, K. A., Williams, R. J. R., Batha, C. A., Kuchugov, P. A., Ladonkina, M. E., Tishkin, V. F., Zmitrenko, N. V., Rozanov, V. B., and Youngs, D. L.
```*Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ-group collaboration*. United States: N. p., 2017.
Web. doi:10.1063/1.4993464.

```
Thornber, B., Griffond, J., Poujade, O., Attal, N., Varshochi, H., Bigdelou, P., Ramaprabhu, P., Olson, B., Greenough, J., Zhou, Y., Schilling, O., Garside, K. A., Williams, R. J. R., Batha, C. A., Kuchugov, P. A., Ladonkina, M. E., Tishkin, V. F., Zmitrenko, N. V., Rozanov, V. B., & Youngs, D. L.
```*Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ-group collaboration*. United States. doi:10.1063/1.4993464.

```
Thornber, B., Griffond, J., Poujade, O., Attal, N., Varshochi, H., Bigdelou, P., Ramaprabhu, P., Olson, B., Greenough, J., Zhou, Y., Schilling, O., Garside, K. A., Williams, R. J. R., Batha, C. A., Kuchugov, P. A., Ladonkina, M. E., Tishkin, V. F., Zmitrenko, N. V., Rozanov, V. B., and Youngs, D. L. Mon .
"Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ-group collaboration". United States. doi:10.1063/1.4993464. https://www.osti.gov/servlets/purl/1468910.
```

```
@article{osti_1468910,
```

title = {Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ-group collaboration},

author = {Thornber, B. and Griffond, J. and Poujade, O. and Attal, N. and Varshochi, H. and Bigdelou, P. and Ramaprabhu, P. and Olson, B. and Greenough, J. and Zhou, Y. and Schilling, O. and Garside, K. A. and Williams, R. J. R. and Batha, C. A. and Kuchugov, P. A. and Ladonkina, M. E. and Tishkin, V. F. and Zmitrenko, N. V. and Rozanov, V. B. and Youngs, D. L.},

abstractNote = {Turbulent Richtmyer–Meshkov instability (RMI) is investigated through a series of high resolution three-dimensional simulations of two initial conditions with eight independent codes. The simulations are initialised with a narrowband perturbation such that instability growth is due to non-linear coupling/backscatter from the energetic modes, thus generating the lowest expected growth rate from a pure RMI. By independently assessing the results from each algorithm and computing ensemble averages of multiple algorithms, the results allow a quantification of key flow properties as well as the uncertainty due to differing numerical approaches. A new analytical model predicting the initial layer growth for a multimode narrowband perturbation is presented, along with two models for the linear and non-linear regimes combined. Overall, the growth rate exponent is determined as θ=0.292±0.009, in good agreement with prior studies; however, the exponent is decaying slowly in time. Also, θ is shown to be relatively insensitive to the choice of mixing layer width measurements. The asymptotic integral molecular mixing measures Θ=0.792±0.014, Ξ=0.800±0.014, and Ψ=0.782±0.013 are lower than some experimental measurements but within the range of prior numerical studies. The flow field is shown to be persistently anisotropic for all algorithms, at the latest time having between 49% and 66% higher kinetic energy in the shock parallel direction compared to perpendicular and does not show any return to isotropy. The plane averaged volume fraction profiles at different time instants collapse reasonably well when scaled by the integral width, implying that the layer can be described by a single length scale and thus a single θ. In conclusion, quantitative data given for both ensemble averages and individual algorithms provide useful benchmark results for future research.},

doi = {10.1063/1.4993464},

journal = {Physics of Fluids},

issn = {1070-6631},

number = 10,

volume = 29,

place = {United States},

year = {2017},

month = {10}

}

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