AN INCOHERENT ALPHA-OMEGA-DYNAMO IN ACCRETION DISKS

We use the mean-held dynamo equations to show that spatially and tempo rally incoherent fluctuations in the helicity in mirror-symmetric turb ulence in a shearing flow can generate a large-scale, coherent magneti c held. We illustrate this effect with simulations of a few simple sys tems. For statistically homogeneous turbulence, we find that the dynam o growth rate is roughly shear)(-2/3)N(eddy)(-1/3)(lambda(eddy)/L(B))( 2/3), where tau(eddy) is the eddy turnover time, tau(shear)(-1) is the local shearing rate, N-eddy is the number of eddies per magnetic doma in, lambda(eddy) is the size of an eddy, and L(B) is the extent of a m agnetic domain perpendicular to the mean flow direction. Even in the p resence 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 tau(shear) > tau(eddy). We also identify a related in coherent dynamo in a system with a stationary distribution of helicity with a high-spatial frequency and an average value of zero. In accret ion disks, the incoherent dynamo can lead to axisymmetric magnetic dom ains 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 exam ple, the Balbus-Hawley instability. However, although it explains the generation of a magnetic field in numerical simulations without signif icant large-scale average helicity and the occasional held reversals, it also predicts that the dimensionless viscosity will scale as simila r to (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.