# TURBULENCE AND STEADY FLOWS IN THREE-DIMENSIONAL GLOBAL STRATIFIED MAGNETOHYDRODYNAMIC SIMULATIONS OF ACCRETION DISKS

## Abstract

We present full 2{pi} global three-dimensional stratified magnetohydrodynamic (MHD) simulations of accretion disks. We interpret our results in the context of protoplanetary disks. We investigate the turbulence driven by the magnetorotational instability (MRI) using the PLUTO Godunov code in spherical coordinates with the accurate and robust HLLD Riemann solver. We follow the turbulence for more than 1500 orbits at the innermost radius of the domain to measure the overall strength of turbulent motions and the detailed accretion flow pattern. We find that regions within two scale heights of the midplane have a turbulent Mach number of about 0.1 and a magnetic pressure two to three orders of magnitude less than the gas pressure, while in those outside three scale heights the magnetic pressure equals or exceeds the gas pressure and the turbulence is transonic, leading to large density fluctuations. The strongest large-scale density disturbances are spiral density waves, and the strongest of these waves has m = 5. No clear meridional circulation appears in the calculations because fluctuating radial pressure gradients lead to changes in the orbital frequency, comparable in importance to the stress gradients that drive the meridional flows in viscous models. The net mass flow rate is wellmore »

- Authors:

- Max Planck Institute for Astronomy, Koenigstuhl 17, 69117 Heidelberg (Germany)

- Publication Date:

- OSTI Identifier:
- 21578369

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal

- Additional Journal Information:
- Journal Volume: 735; Journal Issue: 2; Other Information: DOI: 10.1088/0004-637X/735/2/122; Journal ID: ISSN 0004-637X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCRETION DISKS; DENSITY; DISTURBANCES; FLOW RATE; INSTABILITY; MAGNETIC FIELDS; MAGNETIC RECONNECTION; MAGNETOHYDRODYNAMICS; MASS; PRESSURE GRADIENTS; PROTOPLANETS; SIMULATION; THREE-DIMENSIONAL CALCULATIONS; TURBULENCE; FLUID MECHANICS; HYDRODYNAMICS; MECHANICS; PHYSICAL PROPERTIES

### Citation Formats

```
Flock, M., Dzyurkevich, N., Klahr, H., Turner, N. J., and Henning, Th..
```*TURBULENCE AND STEADY FLOWS IN THREE-DIMENSIONAL GLOBAL STRATIFIED MAGNETOHYDRODYNAMIC SIMULATIONS OF ACCRETION DISKS*. United States: N. p., 2011.
Web. doi:10.1088/0004-637X/735/2/122.

```
Flock, M., Dzyurkevich, N., Klahr, H., Turner, N. J., & Henning, Th..
```*TURBULENCE AND STEADY FLOWS IN THREE-DIMENSIONAL GLOBAL STRATIFIED MAGNETOHYDRODYNAMIC SIMULATIONS OF ACCRETION DISKS*. United States. doi:10.1088/0004-637X/735/2/122.

```
Flock, M., Dzyurkevich, N., Klahr, H., Turner, N. J., and Henning, Th.. Sun .
"TURBULENCE AND STEADY FLOWS IN THREE-DIMENSIONAL GLOBAL STRATIFIED MAGNETOHYDRODYNAMIC SIMULATIONS OF ACCRETION DISKS". United States. doi:10.1088/0004-637X/735/2/122.
```

```
@article{osti_21578369,
```

title = {TURBULENCE AND STEADY FLOWS IN THREE-DIMENSIONAL GLOBAL STRATIFIED MAGNETOHYDRODYNAMIC SIMULATIONS OF ACCRETION DISKS},

author = {Flock, M. and Dzyurkevich, N. and Klahr, H. and Turner, N. J. and Henning, Th.},

abstractNote = {We present full 2{pi} global three-dimensional stratified magnetohydrodynamic (MHD) simulations of accretion disks. We interpret our results in the context of protoplanetary disks. We investigate the turbulence driven by the magnetorotational instability (MRI) using the PLUTO Godunov code in spherical coordinates with the accurate and robust HLLD Riemann solver. We follow the turbulence for more than 1500 orbits at the innermost radius of the domain to measure the overall strength of turbulent motions and the detailed accretion flow pattern. We find that regions within two scale heights of the midplane have a turbulent Mach number of about 0.1 and a magnetic pressure two to three orders of magnitude less than the gas pressure, while in those outside three scale heights the magnetic pressure equals or exceeds the gas pressure and the turbulence is transonic, leading to large density fluctuations. The strongest large-scale density disturbances are spiral density waves, and the strongest of these waves has m = 5. No clear meridional circulation appears in the calculations because fluctuating radial pressure gradients lead to changes in the orbital frequency, comparable in importance to the stress gradients that drive the meridional flows in viscous models. The net mass flow rate is well reproduced by a viscous model using the mean stress distribution taken from the MHD calculation. The strength of the mean turbulent magnetic field is inversely proportional to the radius, so the fields are approximately force-free on the largest scales. Consequently, the accretion stress falls off as the inverse square of the radius.},

doi = {10.1088/0004-637X/735/2/122},

journal = {Astrophysical Journal},

issn = {0004-637X},

number = 2,

volume = 735,

place = {United States},

year = {2011},

month = {7}

}