# EXTENDED SCALING LAWS IN NUMERICAL SIMULATIONS OF MAGNETOHYDRODYNAMIC TURBULENCE

## Abstract

Magnetized turbulence is ubiquitous in astrophysical systems, where it notoriously spans a broad range of spatial scales. Phenomenological theories of MHD turbulence describe the self-similar dynamics of turbulent fluctuations in the inertial range of scales. Numerical simulations serve to guide and test these theories. However, the computational power that is currently available restricts the simulations to Reynolds numbers that are significantly smaller than those in astrophysical settings. In order to increase computational efficiency and, therefore, probe a larger range of scales, one often takes into account the fundamental anisotropy of field-guided MHD turbulence, with gradients being much slower in the field-parallel direction. The simulations are then optimized by employing the reduced MHD equations and relaxing the field-parallel numerical resolution. In this work we explore a different possibility. We propose that there exist certain quantities that are remarkably stable with respect to the Reynolds number. As an illustration, we study the alignment angle between the magnetic and velocity fluctuations in MHD turbulence, measured as the ratio of two specially constructed structure functions. We find that the scaling of this ratio can be extended surprisingly well into the regime of relatively low Reynolds number. However, the extended scaling easily becomes spoiled whenmore »

- Authors:

- Department of Astronomy and Astrophysics, University of Chicago, 5640 S. Ellis Ave, Chicago, IL 60637 (United States)
- Department of Physics, University of Wisconsin at Madison, 1150 University Ave, Madison, WI 53706 (United States)

- Publication Date:

- OSTI Identifier:
- 21562560

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal Letters

- Additional Journal Information:
- Journal Volume: 735; Journal Issue: 2; Other Information: DOI: 10.1088/2041-8205/735/2/L26; Journal ID: ISSN 2041-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANISOTROPY; COMPUTERIZED SIMULATION; FLUCTUATIONS; MAGNETOHYDRODYNAMICS; REYNOLDS NUMBER; SCALING LAWS; TURBULENCE; VELOCITY; DIMENSIONLESS NUMBERS; FLUID MECHANICS; HYDRODYNAMICS; MECHANICS; SIMULATION; VARIATIONS

### Citation Formats

```
Mason, Joanne, Cattaneo, Fausto, Perez, Jean Carlos, and Boldyrev, Stanislav, E-mail: jmason@flash.uchicago.edu, E-mail: cattaneo@flash.uchicago.edu, E-mail: jcperez@wisc.edu, E-mail: boldyrev@wisc.edu.
```*EXTENDED SCALING LAWS IN NUMERICAL SIMULATIONS OF MAGNETOHYDRODYNAMIC TURBULENCE*. United States: N. p., 2011.
Web. doi:10.1088/2041-8205/735/2/L26.

```
Mason, Joanne, Cattaneo, Fausto, Perez, Jean Carlos, & Boldyrev, Stanislav, E-mail: jmason@flash.uchicago.edu, E-mail: cattaneo@flash.uchicago.edu, E-mail: jcperez@wisc.edu, E-mail: boldyrev@wisc.edu.
```*EXTENDED SCALING LAWS IN NUMERICAL SIMULATIONS OF MAGNETOHYDRODYNAMIC TURBULENCE*. United States. doi:10.1088/2041-8205/735/2/L26.

```
Mason, Joanne, Cattaneo, Fausto, Perez, Jean Carlos, and Boldyrev, Stanislav, E-mail: jmason@flash.uchicago.edu, E-mail: cattaneo@flash.uchicago.edu, E-mail: jcperez@wisc.edu, E-mail: boldyrev@wisc.edu. Sun .
"EXTENDED SCALING LAWS IN NUMERICAL SIMULATIONS OF MAGNETOHYDRODYNAMIC TURBULENCE". United States. doi:10.1088/2041-8205/735/2/L26.
```

```
@article{osti_21562560,
```

title = {EXTENDED SCALING LAWS IN NUMERICAL SIMULATIONS OF MAGNETOHYDRODYNAMIC TURBULENCE},

author = {Mason, Joanne and Cattaneo, Fausto and Perez, Jean Carlos and Boldyrev, Stanislav, E-mail: jmason@flash.uchicago.edu, E-mail: cattaneo@flash.uchicago.edu, E-mail: jcperez@wisc.edu, E-mail: boldyrev@wisc.edu},

abstractNote = {Magnetized turbulence is ubiquitous in astrophysical systems, where it notoriously spans a broad range of spatial scales. Phenomenological theories of MHD turbulence describe the self-similar dynamics of turbulent fluctuations in the inertial range of scales. Numerical simulations serve to guide and test these theories. However, the computational power that is currently available restricts the simulations to Reynolds numbers that are significantly smaller than those in astrophysical settings. In order to increase computational efficiency and, therefore, probe a larger range of scales, one often takes into account the fundamental anisotropy of field-guided MHD turbulence, with gradients being much slower in the field-parallel direction. The simulations are then optimized by employing the reduced MHD equations and relaxing the field-parallel numerical resolution. In this work we explore a different possibility. We propose that there exist certain quantities that are remarkably stable with respect to the Reynolds number. As an illustration, we study the alignment angle between the magnetic and velocity fluctuations in MHD turbulence, measured as the ratio of two specially constructed structure functions. We find that the scaling of this ratio can be extended surprisingly well into the regime of relatively low Reynolds number. However, the extended scaling easily becomes spoiled when the dissipation range in the simulations is underresolved. Thus, taking the numerical optimization methods too far can lead to spurious numerical effects and erroneous representation of the physics of MHD turbulence, which in turn can affect our ability to identify correctly the physical mechanisms that are operating in astrophysical systems.},

doi = {10.1088/2041-8205/735/2/L26},

journal = {Astrophysical Journal Letters},

issn = {2041-8205},

number = 2,

volume = 735,

place = {United States},

year = {2011},

month = {7}

}