Blowout bifurcations and the onset of magnetic dynamo action

This paper numerically investigates the magnetohydrodynamic equations in three dimensions with periodic boundary conditions in a parameter range where a forced fluid flow is chaotic. It is found that the transition to dynamo action, whereby the magnetic field is sustained by interaction with the forced flow, is a blowout bifurcation. The blowout bifurcation is typified by bursting behavior, or “on-off intermittency.” In particular, near the transition there are short, intermittently occurring bursts of strong magnetic field activity where the total magnetic energy is comparable to the total flow kinetic energy. Between these bursts the magnetic energy is very small. As one approaches the transition from the dynamo-active side, the time between bursts becomes longer and longer, approaching infinity at the transition. Numerical verification is given for the presence of signature scaling laws in numerical computations utilizing a pseudospectral model with triply periodic boundary conditions. This work implies specific testable predictions for experimental dynamos.