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

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

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