# Three-Dimensional Simulations of Kelvin-Helmholtz Instability in Settled Dust Layers in Protoplanetary Disks

**Authors:** Joseph A. Barranco  
**arXiv:** [0711.4410](https://arxiv.org/abs/0711.4410)  
**Date:** 2007-11-28  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/0711.4410v1/

## Key points

- Study conducted by Joseph A. Barranco from San Francisco State University
- Investigation of Kelvin-Helmholtz instability in dust layers within protoplanetary disks using 3D simulations
- Development of vertical shear due to differing velocities of dust-rich gas in the midplane and dust-depleted gas above and below
- Coriolis force increases instability of dust layers without radial shear, especially at high spatial wavenumbers for thicker layers
- Introduction of radial shear alters onset of instability based on perturbation amplitudes
- Thinner and more unstable layers show a sharp decrease in critical amplitude for instability onset
- Turbulence plays a crucial role in mixing dust and gas, creating thicker and more stable layers
- Layers with minimum Richardson numbers ranging from 0.2 to 0.4 remain stable when horizontal shear is present

## Summary

In a study conducted by Joseph A. Barranco from San Francisco State University, 3D simulations were used to investigate the Kelvin-Helmholtz instability in dust layers within protoplanetary disks. As dust settles in these disks, a vertical shear develops due to differing velocities of dust-rich gas in the midplane and dust-depleted gas above and below. Previous analyses suggested that the Richardson number must be below one-quarter for Kelvin-Helmholtz instability to occur in stratified shear flows. However, numerical studies indicated that the Coriolis force may increase instability while horizontal shear could have a stabilizing effect. Through simulations with a 3D spectral code, Barranco aimed to understand how these opposing forces impact the instability and whether conditions could lead to gravitational instability within these layers. The results confirmed that the Coriolis force increases the instability of dust layers without radial shear, especially at high spatial wavenumbers for thicker layers. Introducing radial shear altered the onset of instability based on perturbation amplitudes: small perturbations were sheared to high wavenumbers where growth was dampened, while larger perturbations disrupted the dust layer. Interestingly, thinner and more unstable layers showed a sharp decrease in critical amplitude for instability onset. In simulations of unstable layers, turbulence played a crucial role in mixing dust and gas, ultimately creating thicker and more stable layers. Notably, Barranco found that layers with minimum Richardson numbers ranging from 0.2 to 0.4 remained stable when horizontal shear was present in simulations. This research sheds light on the complex interplay between various forces affecting dust layer stability within protoplanetary disks and provides valuable insights into how turbulence and shear dynamics influence their evolution.