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

## Abstract

Data from a 1152X760X1280 direct numerical simulation (DNS) of a transitional Rayleigh-Taylor mixing layer modeled after a small Atwood number water channel experiment is used to comprehensively investigate the structure of mean and turbulent transport and mixing. The simulation had physical parameters and initial conditions approximating those in the experiment. The budgets of the mean vertical momentum, heavy-fluid mass fraction, turbulent kinetic energy, turbulent kinetic energy dissipation rate, heavy-fluid mass fraction variance, and heavy-fluid mass fraction variance dissipation rate equations are constructed using Reynolds averaging applied to the DNS data. The relative importance of mean and turbulent production, turbulent dissipation and destruction, and turbulent transport are investigated as a function of Reynolds number and across the mixing layer to provide insight into the flow dynamics not presently available from experiments. The analysis of the budgets supports the assumption for small Atwood number, Rayleigh/Taylor driven flows that the principal transport mechanisms are buoyancy production, turbulent production, turbulent dissipation, and turbulent diffusion (shear and mean field production are negligible). As the Reynolds number increases, the turbulent production in the turbulent kinetic energy dissipation rate equation becomes the dominant production term, while the buoyancy production plateaus. Distinctions between momentum and scalar transport aremore »

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Texas A & M Univ., College Station, TX (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1076443

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics of Fluids (1994)

- Additional Journal Information:
- Journal Volume: 22; Journal Issue: 10; Journal ID: ISSN 1070-6631

- Publisher:
- American Institute of Physics

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; turbulent flow; turbulent transport processes; turbulent mixing layers; Reynolds stress modeling; flow instabilities

### Citation Formats

```
Schilling, Oleg, and Mueschke, Nicholas J.
```*Analysis of turbulent transport and mixing in transitional Rayleigh–Taylor unstable flow using direct numerical simulation data*. United States: N. p., 2010.
Web. doi:10.1063/1.3484247.

```
Schilling, Oleg, & Mueschke, Nicholas J.
```*Analysis of turbulent transport and mixing in transitional Rayleigh–Taylor unstable flow using direct numerical simulation data*. United States. doi:10.1063/1.3484247.

```
Schilling, Oleg, and Mueschke, Nicholas J. Mon .
"Analysis of turbulent transport and mixing in transitional Rayleigh–Taylor unstable flow using direct numerical simulation data". United States. doi:10.1063/1.3484247. https://www.osti.gov/servlets/purl/1076443.
```

```
@article{osti_1076443,
```

title = {Analysis of turbulent transport and mixing in transitional Rayleigh–Taylor unstable flow using direct numerical simulation data},

author = {Schilling, Oleg and Mueschke, Nicholas J.},

abstractNote = {Data from a 1152X760X1280 direct numerical simulation (DNS) of a transitional Rayleigh-Taylor mixing layer modeled after a small Atwood number water channel experiment is used to comprehensively investigate the structure of mean and turbulent transport and mixing. The simulation had physical parameters and initial conditions approximating those in the experiment. The budgets of the mean vertical momentum, heavy-fluid mass fraction, turbulent kinetic energy, turbulent kinetic energy dissipation rate, heavy-fluid mass fraction variance, and heavy-fluid mass fraction variance dissipation rate equations are constructed using Reynolds averaging applied to the DNS data. The relative importance of mean and turbulent production, turbulent dissipation and destruction, and turbulent transport are investigated as a function of Reynolds number and across the mixing layer to provide insight into the flow dynamics not presently available from experiments. The analysis of the budgets supports the assumption for small Atwood number, Rayleigh/Taylor driven flows that the principal transport mechanisms are buoyancy production, turbulent production, turbulent dissipation, and turbulent diffusion (shear and mean field production are negligible). As the Reynolds number increases, the turbulent production in the turbulent kinetic energy dissipation rate equation becomes the dominant production term, while the buoyancy production plateaus. Distinctions between momentum and scalar transport are also noted, where the turbulent kinetic energy and its dissipation rate both grow in time and are peaked near the center plane of the mixing layer, while the heavy-fluid mass fraction variance and its dissipation rate initially grow and then begin to decrease as mixing progresses and reduces density fluctuations. All terms in the transport equations generally grow or decay, with no qualitative change in their profile, except for the pressure flux contribution to the total turbulent kinetic energy flux, which changes sign early in time (a countergradient effect). The production-to-dissipation ratios corresponding to the turbulent kinetic energy and heavy-fluid mass fraction variance are large and vary strongly at small evolution times, decrease with time, and nearly asymptote as the flow enters a self-similar regime. The late-time turbulent kinetic energy production-to-dissipation ratio is larger than observed in shear-driven turbulent flows. The order of magnitude estimates of the terms in the transport equations are shown to be consistent with the DNS at late-time, and also confirms both the dominant terms and their evolutionary behavior. Thus, these results are useful for identifying the dynamically important terms requiring closure, and assessing the accuracy of the predictions of Reynolds-averaged Navier-Stokes and large-eddy simulation models of turbulent transport and mixing in transitional Rayleigh-Taylor instability-generated flow.},

doi = {10.1063/1.3484247},

journal = {Physics of Fluids (1994)},

issn = {1070-6631},

number = 10,

volume = 22,

place = {United States},

year = {2010},

month = {10}

}

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