Supercriticality to subcriticality in dynamo transitions

TL;DR

This paper investigates how the nature of dynamo transitions shifts from supercritical to subcritical as the magnetic Prandtl number decreases, using numerical simulations and simplified models to understand the underlying nonlinear mechanisms.

Contribution

It demonstrates the transition change through direct simulations and introduces simple models that replicate this crossover, linking it to nonlinear stability effects.

Findings

Existence of a well-defined boundary in the hysteresis zone separating dynamo and hydrodynamic states.

Dynamo models show a transition from supercritical to subcritical as magnetic Prandtl number varies.

The transition change is related to the influence of nonlinearities on stability.

Abstract

Evidence from numerical simulations suggest that the nature of dynamo transition changes from supercritical to subcritical as the magnetic Prandtl number is decreased. To explore this interesting crossover we first use direct numerical simulations to investigate the hysteresis zone of a subcritical Taylor-Green dynamo. We establish that a well defined boundary exists in this hysteresis region which separates dynamo states from the purely hydrodynamic solution. We then propose simple dynamo models which show similar crossover from supercritical to subcritical dynamo transition as a function of the magnetic Prandtl number. Our models show that the change in the nature of dynamo transition is connected to the stabilizing or de-stabilizing influence of governing non-linearities.