# Statistical properties of Charney-Hasegawa-Mima zonal flows

## Abstract

A theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent plasma transport events in unforced zonal flows is provided within the Charney-Hasegawa-Mima (CHM) model. The governing equation is solved numerically with various prescribed density gradients that are designed to produce different configurations of parallel and anti-parallel streams. Long-lasting vortices form whose flow is governed by the zonal streams. It is found that the numerically generated PDFs can be matched with analytical predictions of PDFs based on the instanton method by removing the autocorrelations from the time series. In many instances, the statistics generated by the CHM dynamics relaxes to Gaussian distributions for both the electrostatic and vorticity perturbations, whereas in areas with strong nonlinear interactions it is found that the PDFs are exponentially distributed.

- Authors:

- Department of Earth and Space Sciences, Chalmers University of Technology, SE-412 96 Göteborg (Sweden)
- Department of Mathematics and Information Sciences, Northumbria University, Newcastle Upon Tyne NE1 8ST (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22410308

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 22; Journal Issue: 5; Other Information: (c) 2015 EURATOM; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; CORRELATION FUNCTIONS; DISTURBANCES; GAUSS FUNCTION; NONLINEAR PROBLEMS; PLASMA; PROBABILITY DENSITY FUNCTIONS; STATISTICS; STRONG INTERACTIONS; TRANSPORT THEORY; VORTICES

### Citation Formats

```
Anderson, Johan, E-mail: anderson.johan@gmail.com, and Botha, G. J. J.
```*Statistical properties of Charney-Hasegawa-Mima zonal flows*. United States: N. p., 2015.
Web. doi:10.1063/1.4919852.

```
Anderson, Johan, E-mail: anderson.johan@gmail.com, & Botha, G. J. J.
```*Statistical properties of Charney-Hasegawa-Mima zonal flows*. United States. doi:10.1063/1.4919852.

```
Anderson, Johan, E-mail: anderson.johan@gmail.com, and Botha, G. J. J. Fri .
"Statistical properties of Charney-Hasegawa-Mima zonal flows". United States. doi:10.1063/1.4919852.
```

```
@article{osti_22410308,
```

title = {Statistical properties of Charney-Hasegawa-Mima zonal flows},

author = {Anderson, Johan, E-mail: anderson.johan@gmail.com and Botha, G. J. J.},

abstractNote = {A theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent plasma transport events in unforced zonal flows is provided within the Charney-Hasegawa-Mima (CHM) model. The governing equation is solved numerically with various prescribed density gradients that are designed to produce different configurations of parallel and anti-parallel streams. Long-lasting vortices form whose flow is governed by the zonal streams. It is found that the numerically generated PDFs can be matched with analytical predictions of PDFs based on the instanton method by removing the autocorrelations from the time series. In many instances, the statistics generated by the CHM dynamics relaxes to Gaussian distributions for both the electrostatic and vorticity perturbations, whereas in areas with strong nonlinear interactions it is found that the PDFs are exponentially distributed.},

doi = {10.1063/1.4919852},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 5,

volume = 22,

place = {United States},

year = {2015},

month = {5}

}