# Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing

## Abstract

The three-equation k-L-a turbulence model [B. Morgan and M. Wickett, Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meshkov instabilities," Phys. Rev. E 91 (2015)] is extended by the addition of a second length scale equation. It is shown that the separation of turbulence transport and turbulence destruction length scales is necessary for simultaneous prediction of the growth parameter and turbulence intensity of a Kelvin-Helmholtz shear layer when model coeficients are constrained by similarity analysis. Constraints on model coeficients are derived that satisfy an ansatz of self-similarity in the low-Atwood-number limit and allow the determination of model coeficients necessary to recover expected experimental behavior. The model is then applied in one-dimensional simulations of Rayleigh-Taylor, reshocked Richtmyer-Meshkov, Kelvin{Helmholtz, and combined Rayleigh-Taylor/Kelvin-Helmholtz instability mixing layers to demonstrate that the expected growth rates are recovered numerically. Finally, it is shown that model behavior in the case of combined instability is to predict a mixing width that is a linear combination of Rayleigh-Taylor and Kelvin-Helmholtz mixing processes.

- 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

- OSTI Identifier:
- 1430927

- Alternate Identifier(s):
- OSTI ID: 1416418

- Report Number(s):
- LLNL-JRNL-740721

Journal ID: ISSN 2470-0045; PLEEE8

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review E

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 1; Journal ID: ISSN 2470-0045

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

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

### Citation Formats

```
Morgan, Brandon E., Schilling, Oleg, and Hartland, Tucker A..
```*Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevE.97.013104.

```
Morgan, Brandon E., Schilling, Oleg, & Hartland, Tucker A..
```*Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing*. United States. doi:10.1103/PhysRevE.97.013104.

```
Morgan, Brandon E., Schilling, Oleg, and Hartland, Tucker A.. Wed .
"Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing". United States.
doi:10.1103/PhysRevE.97.013104.
```

```
@article{osti_1430927,
```

title = {Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing},

author = {Morgan, Brandon E. and Schilling, Oleg and Hartland, Tucker A.},

abstractNote = {The three-equation k-L-a turbulence model [B. Morgan and M. Wickett, Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meshkov instabilities," Phys. Rev. E 91 (2015)] is extended by the addition of a second length scale equation. It is shown that the separation of turbulence transport and turbulence destruction length scales is necessary for simultaneous prediction of the growth parameter and turbulence intensity of a Kelvin-Helmholtz shear layer when model coeficients are constrained by similarity analysis. Constraints on model coeficients are derived that satisfy an ansatz of self-similarity in the low-Atwood-number limit and allow the determination of model coeficients necessary to recover expected experimental behavior. The model is then applied in one-dimensional simulations of Rayleigh-Taylor, reshocked Richtmyer-Meshkov, Kelvin{Helmholtz, and combined Rayleigh-Taylor/Kelvin-Helmholtz instability mixing layers to demonstrate that the expected growth rates are recovered numerically. Finally, it is shown that model behavior in the case of combined instability is to predict a mixing width that is a linear combination of Rayleigh-Taylor and Kelvin-Helmholtz mixing processes.},

doi = {10.1103/PhysRevE.97.013104},

journal = {Physical Review E},

number = 1,

volume = 97,

place = {United States},

year = {Wed Jan 10 00:00:00 EST 2018},

month = {Wed Jan 10 00:00:00 EST 2018}

}