Evidence for Turbulent Concentration in Particle-laden Midplane Layers of Planet-forming Disks

Abstract

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 ∼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 ≪ 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.