Axisymmetric mean field dynamos with dynamic and algebraic $\alpha$--quenchings

TL;DR

This paper compares axisymmetric mean field dynamo models with dynamic and algebraic alpha-quenching, revealing differences in chaos and multi-attractor behaviors, and highlighting the complex effects of dynamic alpha in spherical systems.

Contribution

It provides a comparative analysis of dynamic and algebraic alpha-quenching in spherical dynamo models, emphasizing their qualitative and quantitative differences and similarities.

Findings

Algebraic alpha-quenching models exhibit chaotic behavior.

Dynamic alpha models can have multi-attractor regimes and sensitivity to initial conditions.

Both models show symmetric, antisymmetric, and mixed modes.

Abstract

We study axisymmetric mean field spherical and spherical shell dynamo models, with both dynamic and algebraic $\alpha$--quenchings. Our results show that there are qualitative as well as quantitative differences and similarities between these models. Regarding similarities, both groups of models exhibit symmetric, antisymmetric and mixed modes of behaviour. As regards differences, the important feature in the full sphere models is the occurrence of chaotic behaviour in the algebraic $\alpha$--quenching models. For the spherical shell models with dynamic $\alpha$ the main features include the possibility of multi-attractor regimes with final state sensitivity with respect to small changes in the magnitude of $\alpha$ and the initial parity. We find the effect of introducing a dynamic $\alpha$ is likely to be complicated and depend on the region of the parameter space considered, rather than a uniform change towards simplicity or complexity.