Evidence For Turbulent Concentration In Particle-Laden Midplane Layers of Planet-Forming Disks

Abstract: In this study we investigate the axisymmetric, weakly turbulent state of settled particle layers in a localized model of a protoplanetary disk. We focus on conditions in which the large-scale axisymmetric filaments typically associated with the streaming instability (SI) either cannot form or have not yet developed. Under these circumstances, we observe small-scale particle clumping consistent with turbulent concentration (TC), in which short particle filaments collect along regions of high gas strain rate and enclose gas-only voids exhibiting coherent vorticity. Despite varying particle Stokes numbers $\St_K$ which are defined relative to the Keplerian frequency, the {\it effective} Stokes numbers within voids, $\St_\omega$ -- defined instead relative to the local gas vorticity -- consistently center around 0.3. The latter coincides with the special value identified in prior statistical studies of TC as the scale where particle clustering is most intermittent. This convergence likely reflects how particle feedback structures and sustains voids -- an effect possibly distinctive to axisymmetric configurations. A timescale comparison reveals that in simulations with midplane particle-to-gas density ratios below unity and $\St_K \ll 1$, SI growth rates are 1 -- 2 orders of magnitude slower than the turbulent overturn frequencies at the driving scale. This disparity appears to effectively rule out SI as the primary driver of turbulence in these cases. Instead, we suggest the Symmetric Instability (SymI) may be responsible. We further observe that for St$_K\ll 1$, TC is a persistent feature of turbulent particle layers , and that Roche-exceeding small-scale fluctuations within large-scale SI filaments reported in the literature are in fact not SI, but expressions of TC amplified by the elevated particle densities within those large-scale structures.