Mean-field dynamos in random Arnold-Beltrami-Childress and Roberts flows

We study magnetic field evolution in flows with fluctuating in time governing parameters in electrically conducting fluid. We use a standard mean-field approach to derive equations for large-scale magnetic field for the fluctuating Arnold-Beltrami-Childress (ABC) flow as well as for the fluctuating Roberts flow. The derived mean-field dynamo equations have growing solutions with growth rate of the large-scale magnetic field which is not controlled by molecular magnetic diffusivity. Our study confirms the Zeldovich idea that the nonstationarity of the fluid flow may remove the obstacle in the large-scale dynamo action of classic stationary flows.