A viscous-convective instability in laminar Keplerian thin discs

TL;DR

This paper investigates how viscous-convective instabilities can develop in thin Keplerian accretion discs, potentially leading to turbulence without magnetic fields, through linear hydrodynamic analysis.

Contribution

It introduces a new analysis of viscous-convective instability in Keplerian discs using the anelastic approximation and Sturm-Liouville eigenvalue problem.

Findings

Overstable modes appear above a critical Prandtl number.

Modes are viscous-convective and can seed turbulence.

Instability occurs even without magnetic fields.

Abstract

Using the anelastic approximation of linearized hydrodynamic equations, we investigate the development of axially symmetric small perturbations in thin Keplerian discs. Dispersion relation is found as a solution of general Sturm-Liouville eigenvalue problem for different values of relevant physical parameters (viscosity, heat conductivity, disc semithickness). The analysis reveals the appearance of overstable mode for Prandtl parameter higher than some critical value. These modes have a viscous-convective nature and can serve as a seed for turbulence in astrophysical discs even in the absence of magnetic fields.