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# Time-dependent study of anisotropy in Rayleigh-Taylor instability induced turbulent flows with a variety of density ratios

## Abstract

This study focuses on understanding the time-dependent anisotropy, mixing, scaling of flows induced by Rayleigh-Taylor instability, and complementing the late-time snapshots reported by Cabot and Zhou [“Statistical measurements of scaling and anisotropy of turbulent flows induced by Rayleigh-Taylor instability,” Phys. Fluids 25, 015107 (2013)]. In particular, we utilize three large datasets with different Atwood numbers (density ratios) from well resolved direct numerical simulations at a moderate Reynolds number with the goal of determining the degree of departure of this inhomogeneous flow from that of homogeneous, isotropic turbulence. Three key time-dependent statistical measurements are considered in detail to delineate the role played by the acceleration. First, a number of directional length scales in this anisotropic turbulence are inspected. Second, the relationship among the outer-scale, the turbulence length, and the Taylor-microscale based Reynolds numbers is also clarified. Lastly, the normalized dissipation rate is employed to inspect the distinctive features of the flow in the inhomogeneous direction parallel to gravity and in the homogeneous perpendicular directions.

- Authors:

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

- Publication Date:

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

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

- OSTI Identifier:
- 1569169

- Report Number(s):
- LLNL-JRNL-774944

Journal ID: ISSN 1070-6631; 966422

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Fluids

- Additional Journal Information:
- Journal Volume: 31; Journal Issue: 8; 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

```
Zhou, Ye, and Cabot, William H. Time-dependent study of anisotropy in Rayleigh-Taylor instability induced turbulent flows with a variety of density ratios. United States: N. p., 2019.
Web. doi:10.1063/1.5110914.
```

```
Zhou, Ye, & Cabot, William H. Time-dependent study of anisotropy in Rayleigh-Taylor instability induced turbulent flows with a variety of density ratios. United States. doi:10.1063/1.5110914.
```

```
Zhou, Ye, and Cabot, William H. Tue .
"Time-dependent study of anisotropy in Rayleigh-Taylor instability induced turbulent flows with a variety of density ratios". United States. doi:10.1063/1.5110914.
```

```
@article{osti_1569169,
```

title = {Time-dependent study of anisotropy in Rayleigh-Taylor instability induced turbulent flows with a variety of density ratios},

author = {Zhou, Ye and Cabot, William H.},

abstractNote = {This study focuses on understanding the time-dependent anisotropy, mixing, scaling of flows induced by Rayleigh-Taylor instability, and complementing the late-time snapshots reported by Cabot and Zhou [“Statistical measurements of scaling and anisotropy of turbulent flows induced by Rayleigh-Taylor instability,” Phys. Fluids 25, 015107 (2013)]. In particular, we utilize three large datasets with different Atwood numbers (density ratios) from well resolved direct numerical simulations at a moderate Reynolds number with the goal of determining the degree of departure of this inhomogeneous flow from that of homogeneous, isotropic turbulence. Three key time-dependent statistical measurements are considered in detail to delineate the role played by the acceleration. First, a number of directional length scales in this anisotropic turbulence are inspected. Second, the relationship among the outer-scale, the turbulence length, and the Taylor-microscale based Reynolds numbers is also clarified. Lastly, the normalized dissipation rate is employed to inspect the distinctive features of the flow in the inhomogeneous direction parallel to gravity and in the homogeneous perpendicular directions.},

doi = {10.1063/1.5110914},

journal = {Physics of Fluids},

number = 8,

volume = 31,

place = {United States},

year = {2019},

month = {8}

}

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Works referenced in this record:

##
Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density

journal, November 1882

- Rayleigh,
- Proceedings of the London Mathematical Society, Vol. s1-14, Issue 1

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

journal, December 2017

- Zhou, Ye
- Physics Reports, Vol. 720-722

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

journal, December 2017

- Zhou, Ye
- Physics Reports, Vol. 723-725

##
Anisotropy in turbulent flows and in turbulent transport

journal, July 2005

- Biferale, Luca; Procaccia, Itamar
- Physics Reports, Vol. 414, Issue 2-3

##
Asymptotic behavior of the mixed mass in Rayleigh–Taylor and Richtmyer–Meshkov instability induced flows

journal, May 2016

- Zhou, Ye; Cabot, William H.; Thornber, Ben
- Physics of Plasmas, Vol. 23, Issue 5

##
The role of hot spot mix in the low-foot and high-foot implosions on the NIF

journal, May 2017

- Ma, T.; Patel, P. K.; Izumi, N.
- Physics of Plasmas, Vol. 24, Issue 5

##
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

##
Statistical measurements of scaling and anisotropy of turbulent flows induced by Rayleigh-Taylor instability

journal, January 2013

- Cabot, W.; Zhou, Ye
- Physics of Fluids, Vol. 25, Issue 1

##
Numerical simulations of two-fluid turbulent mixing at large density ratios and applications to the Rayleigh–Taylor instability

journal, November 2013

- Livescu, D.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 371, Issue 2003

##
Comparison of two- and three-dimensional simulations of miscible Rayleigh-Taylor instability

journal, April 2006

- Cabot, W.
- Physics of Fluids, Vol. 18, Issue 4

##
Modelling turbulent mixing by Rayleigh-Taylor instability

journal, July 1989

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

##
The density ratio dependence of self-similar Rayleigh–Taylor mixing

journal, November 2013

- Youngs, David L.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 371, Issue 2003

##
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

##
Study of ultrahigh Atwood-number Rayleigh–Taylor mixing dynamics using the nonlinear large-eddy simulation method

journal, April 2011

- Burton, Gregory C.
- Physics of Fluids, Vol. 23, Issue 4

##
Density Ratio and Entrainment Effects on Asymptotic Rayleigh–Taylor Instability

journal, December 2017

- Shimony, Assaf; Malamud, Guy; Shvarts, Dov
- Journal of Fluids Engineering, Vol. 140, Issue 5

##
Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities

journal, August 2019

- Zhou, Ye; Clark, Timothy T.; Clark, Daniel S.
- Physics of Plasmas, Vol. 26, Issue 8

##
The effects of forced small-wavelength, finite-bandwidth initial perturbations and miscibility on the turbulent Rayleigh–Taylor instability

journal, December 2015

- Roberts, M. S.; Jacobs, J. W.
- Journal of Fluid Mechanics, Vol. 787

##
A simple experiment to investigate two‐dimensional mixing by Rayleigh–Taylor instability

journal, June 1990

- Andrews, M. J.; Spalding, D. B.
- Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 6

##
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

##
Dynamics of buoyancy-driven flows at moderately high Atwood numbers

journal, April 2016

- Akula, Bhanesh; Ranjan, Devesh
- Journal of Fluid Mechanics, Vol. 795

##
A Critical Analysis of Rayleigh–Taylor Growth Rates

journal, May 2001

- Glimm, J.; Grove, J. W.; Li, X. L.
- Journal of Computational Physics, Vol. 169, Issue 2

##
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

##
Modal model for the nonlinear multimode Rayleigh–Taylor instability

journal, August 1996

- Ofer, D.; Alon, U.; Shvarts, D.
- Physics of Plasmas, Vol. 3, Issue 8

##
High-Reynolds number Rayleigh–Taylor turbulence

journal, January 2009

- Livescu, D.; Ristorcelli, J. R.; Gore, R. A.
- Journal of Turbulence, Vol. 10

##
Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations

journal, August 2007

- Zhou, Ye
- Physics of Plasmas, Vol. 14, Issue 8

##
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

##
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

##
On nonlinear *K-l* and *K* -ε models of turbulence

journal, May 1987

- Speziale, Charles G.
- Journal of Fluid Mechanics, Vol. 178

##
Analytical Methods for the Development of Reynolds-Stress Closures in Turbulence

journal, January 1991

- Speziale, C. G.
- Annual Review of Fluid Mechanics, Vol. 23, Issue 1

##
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

##
On the normalized dissipation parameter in decaying turbulence

journal, March 2017

- Djenidi, L.; Lefeuvre, N.; Kamruzzaman, M.
- Journal of Fluid Mechanics, Vol. 817

##
Statistical Theory of Turbulence

journal, September 1935

- Taylor, G. I.
- Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, Vol. 151, Issue 873

##
Dissipation in Turbulent Flows

journal, January 2015

- Vassilicos, J. Christos
- Annual Review of Fluid Mechanics, Vol. 47, Issue 1

##
On the scaling of the turbulence energy dissipation rate

journal, January 1984

- Sreenivasan, K. R.
- Physics of Fluids, Vol. 27, Issue 5

##
An update on the energy dissipation rate in isotropic turbulence

journal, February 1998

- Sreenivasan, Katepalli R.
- Physics of Fluids, Vol. 10, Issue 2

##
Onset criteria for freely decaying isotropic turbulence

journal, October 2018

- Yoffe, S. R.; McComb, W. D.
- Physical Review Fluids, Vol. 3, Issue 10

##
Spectral imbalance and the normalized dissipation rate of turbulence

journal, April 2007

- Bos, W. J. T.; Shao, L.; Bertoglio, J. -P.
- Physics of Fluids, Vol. 19, Issue 4

##
Measurements of the turbulent energy dissipation rate

journal, March 2002

- Pearson, B. R.; Krogstad, P. -Å.; van de Water, W.
- Physics of Fluids, Vol. 14, Issue 3

##
Renormalization group theory for fluid and plasma turbulence

journal, March 2010

- Zhou, Ye
- Physics Reports, Vol. 488, Issue 1