Turbulence in particle laden midplane layers of planet forming disks

TL;DR

This study investigates turbulence mechanisms in particle layers of planet-forming disks, revealing the roles of Kelvin-Helmholtz and Symmetric Instability in driving turbulence, with implications for the onset of streaming instability.

Contribution

It provides a detailed analysis of turbulence drivers in particle-laden disks, highlighting the conditions under which SymI and KHI dominate and their impact on turbulence development.

Findings

KHI dominates for St=0.2, producing off-midplane rolls.

SymI drives turbulence for St=0.04, especially when Ri<1.

Turbulent energy dissipation occurs at scales less than 6-8 grid points.

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.