Hydrodynamic convection in accretion discs

TL;DR

This study investigates hydrodynamic convection in accretion discs through linear analysis and 3D simulations, revealing its potential to drive outward angular momentum transport and form coherent structures.

Contribution

The paper provides a detailed analysis of hydrodynamic convection in accretion discs, highlighting its role in angular momentum transport and the formation of large-scale structures, using both semi-analytical and numerical methods.

Findings

Hydrodynamic convection can drive outward angular momentum transport.

The sign of angular momentum flux depends on numerical diffusivity.

Coherent structures like convective cells, zonal flows, and vortices form in sustained convection.

Abstract

The prevalence and consequences of convection perpendicular to the plane of accretion discs have been discussed for several decades. Recent simulations combining convection and the magnetorotational instability have given fresh impetus to the debate, as the interplay of the two processes can enhance angular momentum transport, at least in the optically thick outburst stage of dwarf novae. In this paper we seek to isolate and understand the most generic features of disc convection, and so undertake its study in purely hydrodynamical models. First, we investigate the linear phase of the instability, obtaining estimates of the growth rates both semi-analytically, using one-dimensional spectral computations, as well as analytically, using WKBJ methods. Next we perform three-dimensional, vertically stratified, shearing box simulations with the conservative, finite-volume code PLUTO, both with and without explicit diffusion coefficients. We find that hydrodynamic convection can, in general, drive outward angular momentum transport, a result that we confirm with ATHENA, an alternative finite-volume code. Moreover, we establish that the sign of the angular momentum flux is sensitive to the diffusivity of the numerical scheme. Finally, in sustained convection, whereby the system is continuously forced to an unstable state, we observe the formation of various coherent structures, including large- scale and oscillatory convective cells, zonal flows, and small vortices.