An Incoherent α-Ω Dynamo in Accretion Disks

We use the mean-field dynamo equations to show that spatially and temporally incoherent fluctuations in the helicity in mirror-symmetric turbulence in a shearing flow can generate a large-scale, coherent magnetic field. We illustrate this effect with simulations of a few simple systems. For statistically homogeneous turbulence, we find that the dynamo growth rate is roughly τ_eddy^−1/3τ_shear^−2/3N_eddy^−1/3(λ_eddy/L_B)^2/3, where τ_eddy is the eddy turnover time, τ_shear⁻¹ is the local shearing rate, N_eddy is the number of eddies per magnetic domain, λ_eddy is the size of an eddy, and L_B is the extent of a magnetic domain perpendicular to the mean flow direction. Even in the presence of turbulence and shear the dynamo can be stopped by turbulent dissipation if (for example) the eddy scale is close to the magnetic domain scale and τ_shear > τ_eddy. We also identify a related incoherent dynamo in a system with a stationary distribution of helicity with a high-spatial frequency and an average value of zero. In accretion disks, the incoherent dynamo can lead to axisymmetric magnetic domains the radial and vertical dimensions of which will be comparable to the disk height. This process may be responsible for dynamo activity seen in simulations of dynamo-generated turbulence involving, for example, the Balbus-Hawley instability. However, although it explains the generation of a magnetic field in numerical simulations without significant large-scale average helicity and the occasional field reversals, it also predicts that the dimensionless viscosity will scale as ~(h/r)², which is not seen in the simulations. On the other hand, this result is consistent with phenomenological models of accretion disks, although these suggest a slightly shallower dependence on h/r. We discuss some possible resolutions to these contradictions.