# SCALING PROPERTIES OF SMALL-SCALE FLUCTUATIONS IN MAGNETOHYDRODYNAMIC TURBULENCE

## Abstract

Magnetohydrodynamic (MHD) turbulence in the majority of natural systems, including the interstellar medium, the solar corona, and the solar wind, has Reynolds numbers far exceeding the Reynolds numbers achievable in numerical experiments. Much attention is therefore drawn to the universal scaling properties of small-scale fluctuations, which can be reliably measured in the simulations and then extrapolated to astrophysical scales. However, in contrast with hydrodynamic turbulence, where the universal structure of the inertial and dissipation intervals is described by the Kolmogorov self-similarity, the scaling for MHD turbulence cannot be established based solely on dimensional arguments due to the presence of an intrinsic velocity scale—the Alfvén velocity. In this Letter, we demonstrate that the Kolmogorov first self-similarity hypothesis cannot be formulated for MHD turbulence in the same way it is formulated for the hydrodynamic case. Besides profound consequences for the analytical consideration, this also imposes stringent conditions on numerical studies of MHD turbulence. In contrast with the hydrodynamic case, the discretization scale in numerical simulations of MHD turbulence should decrease faster than the dissipation scale, in order for the simulations to remain resolved as the Reynolds number increases.

- Authors:

- Space Science Center, University of New Hampshire, Durham, NH 03824 (United States)
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF (United Kingdom)
- Department of Physics, University of Wisconsin at Madison, 1150 University Avenue, Madison, WI 53706 (United States)
- Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637 (United States)

- Publication Date:

- OSTI Identifier:
- 22364978

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal Letters

- Additional Journal Information:
- Journal Volume: 793; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 2041-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALFVEN WAVES; ASTROPHYSICS; COMPUTERIZED SIMULATION; FLUCTUATIONS; INTERSTELLAR SPACE; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; NUMERICAL ANALYSIS; REYNOLDS NUMBER; SOLAR CORONA; SOLAR WIND; TURBULENCE; VELOCITY

### Citation Formats

```
Perez, Jean Carlos, Mason, Joanne, Boldyrev, Stanislav, and Cattaneo, Fausto, E-mail: jeanc.perez@unh.edu, E-mail: j.mason@exeter.ac.uk, E-mail: boldyrev@wisc.edu, E-mail: cattaneo@flash.uchicago.edu.
```*SCALING PROPERTIES OF SMALL-SCALE FLUCTUATIONS IN MAGNETOHYDRODYNAMIC TURBULENCE*. United States: N. p., 2014.
Web. doi:10.1088/2041-8205/793/1/L13.

```
Perez, Jean Carlos, Mason, Joanne, Boldyrev, Stanislav, & Cattaneo, Fausto, E-mail: jeanc.perez@unh.edu, E-mail: j.mason@exeter.ac.uk, E-mail: boldyrev@wisc.edu, E-mail: cattaneo@flash.uchicago.edu.
```*SCALING PROPERTIES OF SMALL-SCALE FLUCTUATIONS IN MAGNETOHYDRODYNAMIC TURBULENCE*. United States. doi:10.1088/2041-8205/793/1/L13.

```
Perez, Jean Carlos, Mason, Joanne, Boldyrev, Stanislav, and Cattaneo, Fausto, E-mail: jeanc.perez@unh.edu, E-mail: j.mason@exeter.ac.uk, E-mail: boldyrev@wisc.edu, E-mail: cattaneo@flash.uchicago.edu. Sat .
"SCALING PROPERTIES OF SMALL-SCALE FLUCTUATIONS IN MAGNETOHYDRODYNAMIC TURBULENCE". United States. doi:10.1088/2041-8205/793/1/L13.
```

```
@article{osti_22364978,
```

title = {SCALING PROPERTIES OF SMALL-SCALE FLUCTUATIONS IN MAGNETOHYDRODYNAMIC TURBULENCE},

author = {Perez, Jean Carlos and Mason, Joanne and Boldyrev, Stanislav and Cattaneo, Fausto, E-mail: jeanc.perez@unh.edu, E-mail: j.mason@exeter.ac.uk, E-mail: boldyrev@wisc.edu, E-mail: cattaneo@flash.uchicago.edu},

abstractNote = {Magnetohydrodynamic (MHD) turbulence in the majority of natural systems, including the interstellar medium, the solar corona, and the solar wind, has Reynolds numbers far exceeding the Reynolds numbers achievable in numerical experiments. Much attention is therefore drawn to the universal scaling properties of small-scale fluctuations, which can be reliably measured in the simulations and then extrapolated to astrophysical scales. However, in contrast with hydrodynamic turbulence, where the universal structure of the inertial and dissipation intervals is described by the Kolmogorov self-similarity, the scaling for MHD turbulence cannot be established based solely on dimensional arguments due to the presence of an intrinsic velocity scale—the Alfvén velocity. In this Letter, we demonstrate that the Kolmogorov first self-similarity hypothesis cannot be formulated for MHD turbulence in the same way it is formulated for the hydrodynamic case. Besides profound consequences for the analytical consideration, this also imposes stringent conditions on numerical studies of MHD turbulence. In contrast with the hydrodynamic case, the discretization scale in numerical simulations of MHD turbulence should decrease faster than the dissipation scale, in order for the simulations to remain resolved as the Reynolds number increases.},

doi = {10.1088/2041-8205/793/1/L13},

journal = {Astrophysical Journal Letters},

issn = {2041-8205},

number = 1,

volume = 793,

place = {United States},

year = {2014},

month = {9}

}