An Incoherent Dynamo in Accretion Disks

We use the mean-eld dynamo equations to show that spatially and temporally incoherent uctuations in the helicity in mirror-symmetric turbulence in a shearing ow can generate a large scale, coherent magnetic eld. We illustrate this eeect with simulations of a few simple systems. For statistically homogeneous turbulence we nd that the dynamo growth rate is roughly ?2=3 eddy ?1=3 shear N ?1=3 eddy , where eddy is the eddy turnover time, ?1 shear is the local shearing rate, and N eddy is the number of eddies per magnetic domain. 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 shear > 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 whose radial and vertical dimensions 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 eld in numerical simulations without signiicant large scale average helicity, and the occasional eld 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.