Subcritical transition to chaos in liquid metal magnetoconvection*

The motionless conducting state of liquid metal convection with an applied vertical magnetic field confined in a vessel with insulating side walls is known to become linearly unstable at a critical value of the dimensionless temperature difference given by the Rayleigh number Ra. Here, we will present direct numerical simulation results which show that finite-amplitude disturbances can give rise to stable equilibrium solutions beneath the linear stability threshold despite the linear onset branch bifurcating supercritically. Under increased thermal driving, solutions on the linear onset branch lose stability and are attracted to an invariant 2-torus born from a secondary Hopf bifurcation of the subcritical branch, which subsequently follows a Ruelle-Takens-Newhouse route to chaos. Thus, we show that the transition to turbulence is controlled by the subcritical branch, and chaotic solutions have no connection to linear stability theory.