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

Abstract

We investigate the axisymmetric, weakly turbulent state of settled particle layers in a model of a globally laminar protoplanetary disk. We focus on conditions in which the large-scale axisymmetric filaments associated with the streaming instability (SI) either cannot form or have not developed yet. We observe small-scale particle clumping consistent with turbulent concentration (TC), in which particle-rich filaments align with regions of high gas strain rate and enclose gas-only voids exhibiting coherent vorticity. Across a range of particle Stokes numbers, St$_K$ ($0.01-0.04$) -- defined as stopping times relative to the Keplerian frequency -- effective Stokes number within particle voids, St$_ω$, defined instead using local gas vorticity, collapses to values in the range $\sim 0.4-0.7$ for the St$_K$ considered. These values lie close to critical turbulent Stokes numbers associated with maximal clustering intermittency identified in statistical studies of TC. 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 turbulent overturn frequencies at the large-eddy scale, which appears to rule out SI as the primary driver of turbulence here. Instead, we suggest the Symmetric Instability (SymI) may be responsible. We show for our St$_K$ that TC is a persistent feature of our turbulent particle layers, and conclude that small scale particle density fluctuations exceeding the Roche density within large-scale axisymmetric SI filaments reported in the literature are also expressions of TC operating on top of the slightly elevated background particle densities within those large-scale structures.