Turbulence in Particle-laden Midplane Layers of Planet-forming Disks

Abstract

We examine the settled particle layers of planet-forming disks in which the streaming instability (SI) is thought to be either weak or inactive. A suite of low-to-moderate-resolution 3D simulations in a 0.2 H -sized box, where H is the pressure scale height, are performed using PENCIL for two Stokes numbers, St = 0.04 and 0.2, at 1% disk metallicity. We find that a complex of Ekman-layer jet flows emerge subject to three co-acting linearly growing processes: (1) the Kelvin–Helmholtz instability (KHI), (2) the planet-forming disk analog of the baroclinic Symmetric Instability (SymI), and (3) a later-time weakly acting secondary transition process, possibly a manifestation of the SI, producing a radially propagating pattern state. For St = 0.2 KHI is dominant and manifests as off-midplane axisymmetric rolls, while for St = 0.04 the axisymmetric SymI mainly drives turbulence. SymI is analytically developed in a model disk flow, predicting that it becomes strongly active when the Richardson number (Ri) of the particle–gas midplane layer transitions below 1, exhibiting growth rates ≤ 2 / Ri − 2 · Ω , where Ω is the local disk rotation rate. For fairly general situations absent external sources of turbulence it is conjectured that the SI, when and if initiated, emerges out of a turbulent state primarily driven and shaped by at least SymI and/or KHI. We also find that turbulence produced in 256 3 resolution simulations are not statistically converged and that corresponding 512 3 simulations may be converged for St = 0.2. Furthermore, we report that our numerical simulations significantly dissipate turbulent kinetic energy on scales less than six to eight grid points.