# Direct comparisons of compressible magnetohydrodynamics and reduced magnetohydrodynamics turbulence

## Abstract

Direct numerical simulations of low Mach number compressible three-dimensional magnetohydrodynamic (CMHD3D) turbulence in the presence of a strong mean magnetic field are compared with simulations of reduced magnetohydrodynamics (RMHD). Periodic boundary conditions in the three spatial coordinates are considered. Different sets of initial conditions are chosen to explore the applicability of RMHD and to study how close the solution remains to the full compressible MHD solution as both freely evolve in time. In a first set, the initial state is prepared to satisfy the conditions assumed in the derivation of RMHD, namely, a strong mean magnetic field and plane-polarized fluctuations, varying weakly along the mean magnetic field. In those circumstances, simulations show that RMHD and CMHD3D evolve almost indistinguishably from one another. When some of the conditions are relaxed the agreement worsens but RMHD remains fairly close to CMHD3D, especially when the mean magnetic field is large enough. Moreover, the well-known spectral anisotropy effect promotes the dynamical attainment of the conditions for RMHD applicability. Global quantities (mean energies, mean-square current, and vorticity) and energy spectra from the two solutions are compared and point-to-point separation estimations are computed. The specific results shown here give support to the use of RMHD asmore »

- Authors:

- Bartol Research Institute, University of Delaware, Newark, Delaware 19716 (United States)
- (New Zealand)

- Publication Date:

- OSTI Identifier:
- 20782333

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 12; Journal Issue: 11; Other Information: DOI: 10.1063/1.2128573; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANISOTROPY; APPROXIMATIONS; BOUNDARY CONDITIONS; CHARGED-PARTICLE TRANSPORT; COMPARATIVE EVALUATIONS; ELECTRIC CURRENTS; ENERGY SPECTRA; FLUCTUATIONS; MACH NUMBER; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; MATHEMATICAL SOLUTIONS; PERIODICITY; PLASMA; PLASMA SIMULATION; THREE-DIMENSIONAL CALCULATIONS; TURBULENCE; VORTICES

### Citation Formats

```
Dmitruk, Pablo, Matthaeus, William H., Oughton, Sean, and Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton.
```*Direct comparisons of compressible magnetohydrodynamics and reduced magnetohydrodynamics turbulence*. United States: N. p., 2005.
Web. doi:10.1063/1.2128573.

```
Dmitruk, Pablo, Matthaeus, William H., Oughton, Sean, & Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton.
```*Direct comparisons of compressible magnetohydrodynamics and reduced magnetohydrodynamics turbulence*. United States. doi:10.1063/1.2128573.

```
Dmitruk, Pablo, Matthaeus, William H., Oughton, Sean, and Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton. Tue .
"Direct comparisons of compressible magnetohydrodynamics and reduced magnetohydrodynamics turbulence". United States.
doi:10.1063/1.2128573.
```

```
@article{osti_20782333,
```

title = {Direct comparisons of compressible magnetohydrodynamics and reduced magnetohydrodynamics turbulence},

author = {Dmitruk, Pablo and Matthaeus, William H. and Oughton, Sean and Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton},

abstractNote = {Direct numerical simulations of low Mach number compressible three-dimensional magnetohydrodynamic (CMHD3D) turbulence in the presence of a strong mean magnetic field are compared with simulations of reduced magnetohydrodynamics (RMHD). Periodic boundary conditions in the three spatial coordinates are considered. Different sets of initial conditions are chosen to explore the applicability of RMHD and to study how close the solution remains to the full compressible MHD solution as both freely evolve in time. In a first set, the initial state is prepared to satisfy the conditions assumed in the derivation of RMHD, namely, a strong mean magnetic field and plane-polarized fluctuations, varying weakly along the mean magnetic field. In those circumstances, simulations show that RMHD and CMHD3D evolve almost indistinguishably from one another. When some of the conditions are relaxed the agreement worsens but RMHD remains fairly close to CMHD3D, especially when the mean magnetic field is large enough. Moreover, the well-known spectral anisotropy effect promotes the dynamical attainment of the conditions for RMHD applicability. Global quantities (mean energies, mean-square current, and vorticity) and energy spectra from the two solutions are compared and point-to-point separation estimations are computed. The specific results shown here give support to the use of RMHD as a valid approximation of compressible MHD with a mean magnetic field under certain but quite practical conditions.},

doi = {10.1063/1.2128573},

journal = {Physics of Plasmas},

number = 11,

volume = 12,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}