### Leith diffusion model for homogeneous anisotropic turbulence

Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Here, numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.

- Publication Date:

- Report Number(s):
- LA-UR-16-21435

Journal ID: ISSN 0045-7930

- Grant/Contract Number:
- AC52-06NA25396

- Type:
- Accepted Manuscript

- Journal Name:
- Computers and Fluids

- Additional Journal Information:
- Journal Volume: 151; Journal Issue: C; Journal ID: ISSN 0045-7930

- Publisher:
- Elsevier

- Research Org:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org:
- USDOE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; spectral modeling; anisotropic diffusion; anisotropic turbulence

- OSTI Identifier:
- 1338774

- Alternate Identifier(s):
- OSTI ID: 1419375

```
Rubinstein, Robert, Clark, Timothy T., and Kurien, Susan.
```*Leith diffusion model for homogeneous anisotropic turbulence*. United States: N. p.,
Web. doi:10.1016/j.compfluid.2016.07.009.

```
Rubinstein, Robert, Clark, Timothy T., & Kurien, Susan.
```*Leith diffusion model for homogeneous anisotropic turbulence*. United States. doi:10.1016/j.compfluid.2016.07.009.

```
Rubinstein, Robert, Clark, Timothy T., and Kurien, Susan. 2017.
"Leith diffusion model for homogeneous anisotropic turbulence". United States.
doi:10.1016/j.compfluid.2016.07.009. https://www.osti.gov/servlets/purl/1338774.
```

```
@article{osti_1338774,
```

title = {Leith diffusion model for homogeneous anisotropic turbulence},

author = {Rubinstein, Robert and Clark, Timothy T. and Kurien, Susan},

abstractNote = {Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Here, numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.},

doi = {10.1016/j.compfluid.2016.07.009},

journal = {Computers and Fluids},

number = C,

volume = 151,

place = {United States},

year = {2017},

month = {6}

}