Analysis of some preliminary simulations of Keplerian turbulence

Resumen

We present simulations of rotating sheared turbulence both for the Keplerian case, 2Ω/S = 4/3, and for 2Ω/S = −4/3. Both cases are linearly stable, and all the simulations decay, but there is a strong effect of the Reynolds number that is clearly visible in the different long-term behaviors of the simulations in large and in small computational grids. While the latter enter an apparently viscous regime for St = O(1), the former track
the inviscid rapid distortion theory (RDT) solutions for much longer times. The RDT solutions in both cases decay with a similar power-law exponent, −1/2, but the Keplerian case undergoes an appreciable initial transient growth that is absent in the other case.
There are indications of nonlinear growth in a range of wavenumbers that could lead to self-sustaining turbulence in protoplanetary accretion disks. This secondary peak is present for both shear ratios, and is associated in both cases with eddy Rossby numbers of the order of 10−2, and with eddy Reynolds numbers larger than a few hundred. Although additional simulations are needed, the above observations suggest the range of parameters in which to search for self-sustaining Keplerian turbulence, and emphasize the importance of simulations with higher resolutions and Reynolds numbers than those that have been used in the study of this problem up to this point.