We study effects of kinetic helicity fluctuations in a turbulence with
large-scale shear using two different approaches: the spectral
tau-approximation and the second order correlation approximation (or
first-order smoothing approximation). These two approaches demonstrate that
homogeneous kinetic helicity fluctuations alone with zero mean value in a
sheared homogeneous turbulence cannot cause large-scale dynamo. Mean-field
dynamo can be possible when kinetic helicity fluctuations are inhomogeneous
which cause a nonzero mean alpha effect in a sheared turbulence. On the other
hand, shear-current effect can generate large-scale magnetic field even in a
homogeneous nonhelical turbulence with large-scale shear. This effect was
investigated previously for large hydrodynamic and magnetic Reynolds numbers.
In this study we examine the threshold required for the shear-current dynamo
versus Reynolds number. We demonstrate that there is no need for a developed
inertial range in order to maintain the shear-current dynamo (e.g., the
threshold in the Reynolds number is of the order of 1).Comment: 12 pages, 3 Figures, small corrections to match the final published
version, Physical Review E, in pres