  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.
