Nonlinear dynamo in ABC flow: The Hall effect

Nonlinear evolution of the magnetic field generated by a prescribed deterministic flow of a conducting fluid in form of the Arnold--Beltrami--Childress (ABC) flow is studied numerically. The nonlinearity is caused by the Hall effect. After the linear regime, the Hall term in the induction equation becomes important, leading to saturation of the magnetic field. The oscillations of the magnetic field which characterize the linear regime fade away into a steady state regime. The structure of the magnetic field can be viewed as a sum of two components: a field of the integral scale and a small-scale field. The large-scale field contains most of the energy of the system, whereas the energy of the small-scale field is very small. These results demonstrate significant difference between the actions of two types of nonlinearity in terms of the magnetic field: the Ampere force and the Hall effect