Evolution of magnetic field fluctuations in two-dimensional chaotic flow

The two-point correlation tensor of small-scale fluctuations of magnetic field in a two-dimensional chaotic flow is studied. The analytic approach is developed in the framework of the Kraichnan–Kazantsev model. It is shown that the growth of the field fluctuations takes place in an essentially resistive regime and stops at large times in accordance with the so-called anti-dynamo theorems. The value of is enhanced in the course of the evolution by the magnetic Prandtl number.