  It is shown that non-helical (more precisely, parity-invariant) flows capable
of sustaining a large-scale dynamo by the negative magnetic eddy diffusivity
effect are quite common. This conclusion is based on numerical examination of a
large number of randomly selected flows. Few outliers with strongly negative
eddy diffusivities are also found, and they are interpreted in terms of the
closeness of the control parameter to a critical value for generation of a
small-scale magnetic field. Furthermore, it is shown that, for parity-invariant
flows, a moderate separation of scales between the basic flow and the magnetic
field often significantly reduces the critical magnetic Reynolds number for the
onset of dynamo action.
