A viscous instability in axially symmetric laminar shear flows

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.

12 pages, 7 figure, accepted for publication in MNRAS

References in corpus (6)

• The viscosity parameter alpha and the properties of accretion disc outbursts in close binaries
• Viscous, Resistive Magnetorotational Modes
• Viscous overstability and eccentricity evolution in three-dimensional gaseous discs
• Modeling of non-stationary accretion disks in X-ray novae A 0620-00 and GRS 1124-68 during outburst
• A study of transient dynamics of perturbations in Keplerian discs using a variational approach
• On properties of Velikhov-Chandrasekhar MRI in ideal and non-ideal plasma

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• On dynamics of nonmagnetic accretion disks