Rossby Wave Instability in three dimensional discs

TL;DR

This paper provides a linear analysis and numerical validation of the Rossby wave instability in three-dimensional protoplanetary discs, revealing that 3D effects slightly reduce growth rates and match velocity structures.

Contribution

It presents the first detailed linear analysis of 3D RWI in isothermal discs and compares results with numerical simulations, confirming the accuracy of 3D modeling.

Findings

3D RWI growth rates are slightly smaller than 2D

Numerical simulations match linear eigenfunctions

Vortices exhibit significant vertical velocities

Abstract

The Rossby wave instability (RWI) is a promising mechanism for producing large-scale vortices in protoplanetary discs. The instability operates around a density bump in the disc, and the resulting vortices may facilitate planetesimal formation and angular momentum transfer in the disc dead zone. Most previous works on the RWI deal with two-dimensional (height-integrated) discs. However, vortices may have different dynamical behaviours in 3D than in 2D. Recent numerical simulations of the RWI in 3D global discs by Meheut et al. have revealed intriguing vertical structure of the vortices, including appreciable vertical velocities. In this paper we present a linear analysis of the RWI in 3D global models of isothermal discs. We calculate the growth rates of the Rossby modes (of various azimuthal wave numbers m = 2 - 6) trapped around the fiducial density bump and carry out 3D numerical simulations to compare with our linear results. We show that the 3D RWI growth rates are only slightly smaller than the 2D growth rates, and the velocity structures seen in the numerical simulations during the linear phase are in agreement with the velocity eigenfunctions obtained in our linear calculations. This numerical benchmark shows that numerical simulations can accurately describe the instability. The angular momentum transfer rate associated with Rossby vortices is also studied.