# Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime

## Abstract

Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh–Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number,$$A=(\unicode[STIX]{x1D70C}_{2}-\unicode[STIX]{x1D70C}_{1})/(\unicode[STIX]{x1D70C}_{2}+\unicode[STIX]{x1D70C}_{1})$$, where$$\unicode[STIX]{x1D70C}_{2}$$and$$\unicode[STIX]{x1D70C}_{1}$$are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of$A=0.49$$,$$A=0.63$$,$$A=0.82$$and$$A=0.94$$. Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber,$$k=2\unicode[STIX]{x03C0}/\unicode[STIX]{x1D706}=0.247~\text{mm}^{-1}$$, experiments and simulations, where$$\unicode[STIX]{x1D706}$is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov’s model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.

- Authors:

- Univ. of Arizona, Tucson, AZ (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Univ. of Arizona, Tucson, AZ (United States)

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

- Contributing Org.:
- Lawrence Livermore National Laboratory

- OSTI Identifier:
- 1419851

- Grant/Contract Number:
- NA0002929

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Fluid Mechanics

- Additional Journal Information:
- Journal Volume: 838; Journal ID: ISSN 0022-1120

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; gas dynamics; nonlinear instability; turbulent mixing

### Citation Formats

```
Morgan, R. V., Cabot, W. H., Greenough, J. A., and Jacobs, J. W.
```*Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime*. United States: N. p., 2018.
Web. doi:10.1017/jfm.2017.893.

```
Morgan, R. V., Cabot, W. H., Greenough, J. A., & Jacobs, J. W.
```*Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime*. United States. doi:10.1017/jfm.2017.893.

```
Morgan, R. V., Cabot, W. H., Greenough, J. A., and Jacobs, J. W. Fri .
"Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime". United States.
doi:10.1017/jfm.2017.893.
```

```
@article{osti_1419851,
```

title = {Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime},

author = {Morgan, R. V. and Cabot, W. H. and Greenough, J. A. and Jacobs, J. W.},

abstractNote = {Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh–Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number,$A=(\unicode[STIX]{x1D70C}_{2}-\unicode[STIX]{x1D70C}_{1})/(\unicode[STIX]{x1D70C}_{2}+\unicode[STIX]{x1D70C}_{1})$, where$\unicode[STIX]{x1D70C}_{2}$and$\unicode[STIX]{x1D70C}_{1}$are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of$A=0.49$,$A=0.63$,$A=0.82$and$A=0.94$. Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber,$k=2\unicode[STIX]{x03C0}/\unicode[STIX]{x1D706}=0.247~\text{mm}^{-1}$, experiments and simulations, where$\unicode[STIX]{x1D706}$is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov’s model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.},

doi = {10.1017/jfm.2017.893},

journal = {Journal of Fluid Mechanics},

number = ,

volume = 838,

place = {United States},

year = {Fri Jan 12 00:00:00 EST 2018},

month = {Fri Jan 12 00:00:00 EST 2018}

}