The dependence of the viscosity in accretion discs on the shear/vorticity ratio

We estimate the Shakura-Sunyaev viscosity parameter alpha for different values of the shear/vorticity ratio, sigma/omega, using local simulations of dynamo-generated turbulence. We find that the time average of alpha is approximately proportional to sigma/omega (at least for sigma/omega < 10). We point out that this result may have important implications for the properties of thick accretion discs, because there omega is small and alpha would then tend to be large. Our result may also be important for accretion discs around black holes, because sigma/omega becomes large in the inner 10 Schwarzschild radii as a result of relativistic effects.