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

TL;DR

This paper investigates the behavior of magnetic field amplification in a two-dimensional chaotic flow using the Kraichnan-Kazantsev model, revealing the cessation of growth over time and detailing the magnetic field's spatial correlations.

Contribution

It provides an analytical study of the small-scale kinematic dynamo in 2D chaotic flows, including the magnetic field's spatial structure and growth limitations.

Findings

Magnetic field growth halts at large times due to anti-dynamo theorems.

Magnetic field fluctuations increase proportionally to the square of the magnetic Prandtl number.

Spatial correlation tensor of the magnetic field is explicitly derived.

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 $\bm{B}$ fluctuations stops at large times in accordance with so-called anti-dynamo theorems. The value of $\bm{B}^2$ increased therewith in square of the magnetic Prandtl number times. The spatial structure of the correlation tensor of the magnetic field is found.