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 three-dimensional simulations in a $0.2H$ 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 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 $\le\sqrt{2/\Ri - 2}\cdot\Omega$, where $\Omega$ is 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 6-8 grid points.