Subcritical transition and multistability in liquid-metal magnetoconvection with sidewalls

The motionless conducting state of liquid-metal convection with an applied vertical magnetic field confined in a vessel with insulating sidewalls becomes linearly unstable to wall modes through a supercritical pitchfork bifurcation. Nevertheless, we show that the transition proceeds subcritically, with stable finite-amplitude solutions with different symmetries existing at parameter values beneath this linear stability threshold. Under increased thermal driving, the branch born from the linear instability becomes unstable and solutions are attracted to the most subcritical branch, which follows a quasiperiodic route to chaos. Thus, we show that the transition to turbulence is controlled by this subcritical branch and hence turbulent solutions have no connection to the initial linear instability. This is further quantified by observing that the subcritical equilibrium solution sets the spatial symmetry of the turbulent mean flow and thus organises large-scale structures in the turbulent regime.