Supercriticality to subcriticality in dynamo transitions

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.

Version 3 note: Found a sign-error in an equation which propagated further. Section 4 and Fig. 3,4,5 are updated in Version 3 (final form)

References in corpus (6)

• Generation of magnetic field by dynamo action in a turbulent flow of liquid sodium
• A self-sustaining nonlinear dynamo process in Keplerian shear flows
• Dynamo Transition in Low-dimensional Models
• Bistability and chaos in Taylor-Green dynamo
• Axial dipolar dynamo action in the Taylor-Green vortex
• Subcritical dynamo bifurcation in the Taylor Green flow

Cited by in corpus (5)

• Dynamo theories
• Critical Slowing Down at the Abrupt Mott Transition: When the First-Order Phase Transition Becomes Zeroth-Order and Looks Like Second-Order
• Turbulent drag reduction in magnetohydrodynamic and quasi-static magnetohydrodynamic turbulence
• Dynamo transition in a five-mode helical model
• Stochastic bistable systems, and competing hysteresis and phase coexistence