# Leith diffusion model for homogeneous anisotropic turbulence

## Abstract

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.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1338774

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

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

Journal ID: ISSN 0045-7930

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Computers and Fluids

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

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

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

### Citation Formats

```
Rubinstein, Robert, Clark, Timothy T., and Kurien, Susan.
```*Leith diffusion model for homogeneous anisotropic turbulence*. United States: N. p., 2017.
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. Thu .
"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 = {Thu Jun 01 00:00:00 EDT 2017},

month = {Thu Jun 01 00:00:00 EDT 2017}

}

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