Kinematic dynamo in two-dimensional chaotic flow: the initial and final stages

Abstract

The small-scale kinematic dynamo in a two-dimensional chaotic flow is studied. The analytic approach is developed in framework of the Kraichnan-Kazantsev model. It is shown that the growth of magnetic field $\mathbf{B}$ fluctuations stops at large times in accordance with so-called anti-dynamo theorems. The value of ${\mathbf{B}}^2$ increased therewith in square of the magnetic Prandtl number times. The spatial structure of the correlation tensor of the magnetic field is found.

7 pages