  We examine under which conditions one may apply, to steady state keplerian
accretion discs, the "beta"-viscosity prescription which has been derived from
rotating shear flow experiments (Richard & Zahn 1999). Using a vertically
averaged model, we show that this law may be suitable for all three families of
known systems: in young stellar objects, evolved binary stars and Active
Galactic Nuclei discs (except in their outer gas pressure dominated regions
where turbulence becomes hypersonic). According to the standard criterion for
viscous stability, "beta"-discs are always stable throughout. Using realistic
opacities and equation of state, we demonstrate that these discs are thermally
unstable in the temperature domain where hydrogen recombines, when they are
optically thick, and this could lead to limit cycle behavior. Radiation
pressure dominated regions are thermally stable, in contrast with
"alpha"-discs. This results in a fully stable solution for the innermost parts
of AGN discs.
