# Discrete Symmetries in Dynamo Reversals

## TL;DR

This paper uses group theory to classify Fourier modes involved in dynamo reversals, revealing a structured symmetry that explains reversal behaviors in various dynamo experiments and models.

## Contribution

It introduces a novel group-theoretic framework to categorize Fourier modes in dynamo reversals, linking symmetry properties to reversal phenomena.

## Key findings

- Fourier modes form Klein 16-group structure.
- Reversal classes predicted by symmetry analysis match observed reversals.
- Applicable to Taylor-Green dynamo and other models.

## Abstract

Quantification of the velocity and magnetic field reversals in dynamo remains an interesting challenge. In this paper, using group-theoretic analysis, we classify the reversing and non-reversing Fourier modes during a dynamo reversal in a Cartesian box. Based on odd-even parities of the wavenumber indices, we categorise the velocity and magnetic Fourier modes into 8 classes each. Then, using the properties of the nonlinear interactions in magnetohydrodynamics, we show that these 16 elements form Klein 16-group $Z_2 \times Z_2 \times Z_2 \times Z_2$. We demonstrate that field reversals in a class of Taylor-Green dynamo, as well as the reversals in earlier experiments and models, belong to one of the classes predicted by our group-theoretic arguments.