Dynamo Transition in Low-dimensional Models

TL;DR

This paper introduces two simplified low-dimensional magnetohydrodynamic models to study dynamo transitions, revealing how helicity and Prandtl number influence magnetic field generation, aligning with recent numerical and experimental findings.

Contribution

It presents two novel low-dimensional models capturing dynamo transitions influenced by helicity and Prandtl number, providing detailed insights into dynamo mechanisms.

Findings

Dynamo transition depends on forcing amplitude and Prandtl number.

Nonhelical model requires magnetic Prandtl number > 1 for dynamo.

Helical model exhibits dynamo for all magnetic Prandtl numbers.

Abstract

Two low-dimensional magnetohydrodynamic models containing three velocity and three magnetic modes are described. One of them (nonhelical model) has zero kinetic and current helicity, while the other model (helical) has nonzero kinetic and current helicity. The velocity modes are forced in both these models. These low-dimensional models exhibit a dynamo transition at a critical forcing amplitude that depends on the Prandtl number. In the nonhelical model, dynamo exists only for magnetic Prandtl number beyond 1, while the helical model exhibits dynamo for all magnetic Prandtl number. Although the model is far from reproducing all the possible features of dynamo mechanisms, its simplicity allows a very detailed study and the observed dynamo transition is shown to bear similarities with recent numerical and experimental results.