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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