A viscous instability in axially symmetric laminar shear flows

TL;DR

This paper identifies a viscous instability in axisymmetric laminar shear flows around gravitating centers, suggesting it could induce turbulence in astrophysical accretion disks without magnetic fields.

Contribution

It introduces a new viscous instability mechanism in hydrodynamic flows, derived from linearized equations with microscopic transport coefficients, applicable to accretion disk turbulence.

Findings

Viscosity destabilizes one Rayleigh mode in thin accretion flows.

The instability growth rate is a few Keplerian periods at certain wavelengths.

The X-mode remains stable under the studied conditions.

Abstract

A viscous instability in shearing laminar axisymmetric hydrodynamic flows around a gravitating center is described. In the linearized hydrodynamic equations written in the Boussinesq approximation with microscopic molecular transport coefficients, the instability arises when the viscous dissipation is taken into account in the energy equation. Using the local WKB approximation, we derive a third-order algebraic dispersion equation with two modes representing the modified Rayleigh modes R+ and R-, and the third X-mode. We show that in thin accretion flows the viscosity destabilizes one of the Rayleigh modes in a wide range of wavenumbers, while the X-mode always remains stable. In Keplerian flows, the instability increment is found to be a few Keplerian rotational periods at wavelengths with $kr\sim 10-50$. This instability may cause turbulence in astrophysical accretion discs even in the absence of magnetic field.