# Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics

## Abstract

Zonal flows have been observed to appear spontaneously from turbulence in a number of physical settings. A complete theory for their behavior is still lacking. Recently, a number of studies have investigated the dynamics of zonal flows using quasilinear (QL) theories and the statistical framework of a second-order cumulant expansion (CE2). A geometrical-optics (GO) reduction of CE2, derived under an assumption of separation of scales between the fluctuations and the zonal flow, is studied here numerically. The reduced model, CE2-GO, has a similar phase-space mathematical structure to the traditional wave-kinetic equation, but that wave-kinetic equation has been shown to fail to preserve enstrophy conservation and to exhibit an ultraviolet catastrophe. CE2-GO, in contrast, preserves nonlinear conservation of both energy and enstrophy. We show here how to retain these conservation properties in a pseudospectral simulation of CE2-GO. We then present nonlinear simulations of CE2-GO and compare with direct simulations of quasilinear (QL) dynamics. Furthermore, we find that CE2-GO retains some similarities to QL.

- 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 National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1466924

- Alternate Identifier(s):
- OSTI ID: 1427890

- Report Number(s):
- LLNL-JRNL-742576

Journal ID: ISSN 1070-664X; 897424

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 5; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

### Citation Formats

```
Parker, Jeffrey B.
```*Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics*. United States: N. p., 2018.
Web. doi:10.1063/1.5018142.

```
Parker, Jeffrey B.
```*Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics*. United States. doi:10.1063/1.5018142.

```
Parker, Jeffrey B. Thu .
"Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics". United States. doi:10.1063/1.5018142. https://www.osti.gov/servlets/purl/1466924.
```

```
@article{osti_1466924,
```

title = {Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics},

author = {Parker, Jeffrey B.},

abstractNote = {Zonal flows have been observed to appear spontaneously from turbulence in a number of physical settings. A complete theory for their behavior is still lacking. Recently, a number of studies have investigated the dynamics of zonal flows using quasilinear (QL) theories and the statistical framework of a second-order cumulant expansion (CE2). A geometrical-optics (GO) reduction of CE2, derived under an assumption of separation of scales between the fluctuations and the zonal flow, is studied here numerically. The reduced model, CE2-GO, has a similar phase-space mathematical structure to the traditional wave-kinetic equation, but that wave-kinetic equation has been shown to fail to preserve enstrophy conservation and to exhibit an ultraviolet catastrophe. CE2-GO, in contrast, preserves nonlinear conservation of both energy and enstrophy. We show here how to retain these conservation properties in a pseudospectral simulation of CE2-GO. We then present nonlinear simulations of CE2-GO and compare with direct simulations of quasilinear (QL) dynamics. Furthermore, we find that CE2-GO retains some similarities to QL.},

doi = {10.1063/1.5018142},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 5,

volume = 25,

place = {United States},

year = {2018},

month = {3}

}

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