Impact of magneto-rotational instability on grain growth in protoplanetary disks: I. Relevant turbulence properties. (arXiv:2002.05172v1 [astro-ph.SR])

<a href="http://arxiv.org/find/astro-ph/1/au:+Gong_M/0/1/0/all/0/1">Munan Gong</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Ivlev_A/0/1/0/all/0/1">Alexei V. Ivlev</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Zhao_B/0/1/0/all/0/1">Bo Zhao</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Caselli_P/0/1/0/all/0/1">Paola Caselli</a>

Turbulence in the protoplanetary disks induces collisions between dust

grains, and thus facilitates grain growth. We investigate the two fundamental

assumptions of the turbulence in obtaining grain collisional velocities — the

kinetic energy spectrum and the turbulence autocorrelation time — in the

context of the turbulence generated by the magneto-rotational instability

(MRI). We carry out numerical simulations of the MRI as well as driven

turbulence, for a range of physical and numerical parameters. We find that the

convergence of the turbulence $alpha$-parameter does not necessarily imply the

convergence of the energy spectrum. The MRI turbulence is largely solenoidal,

for which we observe a persistent kinetic energy spectrum of $k^{-4/3}$. The

same is obtained for solenoidal driven turbulence with and without magnetic

field, over more than 1 dex near the dissipation scale. This power-law slope

appears to be converged in terms of numerical resolution, and to be due to the

bottleneck effect. The kinetic energy in the MRI turbulence peaks at the

fastest growing mode of the MRI. In contrast, the magnetic energy peaks at the

dissipation scale. The magnetic energy spectrum in the MRI turbulence does not

show a clear power-law range, and is almost constant over approximately 1 dex

near the dissipation scale. The turbulence autocorrelation time is nearly

constant at large scales, limited by the shearing timescale, and shows a

power-law drop close to $k^{-1}$ at small scales, with a slope steeper than

that of the eddy crossing time. The deviation from the standard picture of the

Kolmogorov turbulence with the injection scale at the disk scale height can

potentially have a significant impact on the grain collisional velocities.

Turbulence in the protoplanetary disks induces collisions between dust

grains, and thus facilitates grain growth. We investigate the two fundamental

assumptions of the turbulence in obtaining grain collisional velocities — the

kinetic energy spectrum and the turbulence autocorrelation time — in the

context of the turbulence generated by the magneto-rotational instability

(MRI). We carry out numerical simulations of the MRI as well as driven

turbulence, for a range of physical and numerical parameters. We find that the

convergence of the turbulence $alpha$-parameter does not necessarily imply the

convergence of the energy spectrum. The MRI turbulence is largely solenoidal,

for which we observe a persistent kinetic energy spectrum of $k^{-4/3}$. The

same is obtained for solenoidal driven turbulence with and without magnetic

field, over more than 1 dex near the dissipation scale. This power-law slope

appears to be converged in terms of numerical resolution, and to be due to the

bottleneck effect. The kinetic energy in the MRI turbulence peaks at the

fastest growing mode of the MRI. In contrast, the magnetic energy peaks at the

dissipation scale. The magnetic energy spectrum in the MRI turbulence does not

show a clear power-law range, and is almost constant over approximately 1 dex

near the dissipation scale. The turbulence autocorrelation time is nearly

constant at large scales, limited by the shearing timescale, and shows a

power-law drop close to $k^{-1}$ at small scales, with a slope steeper than

that of the eddy crossing time. The deviation from the standard picture of the

Kolmogorov turbulence with the injection scale at the disk scale height can

potentially have a significant impact on the grain collisional velocities.

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