The validity of the standard alpha viscosity prescription in turbulent
accretion discs is briefly analysed. It is found that the alpha visco
sity prescription is no longer valid when the rotation law of the disc
is not Keplerian. The analysis is based on simple scaling arguments f
or fully developed turbulences in accretion discs. An analytical treat
ment is carried out for geometrically thin non-Keplerian discs in vert
ical hydrostatic equilibrium. The analytical expression of the viscosi
ty is compared with standard values of the viscosity in boundary layer
regions and with the viscosity prescription derived from a general ca
usal equation for the evolution of the stress tenser.