Turbulent magnetohydrodynamic dynamo action in a spherically bounded von Kármán flow at small magnetic Prandtl numbers

Turbulent magnetohydrodynamic (MHD) dynamo action in a spherically bounded electrically conducting flow is investigated numerically. A large-scale two-vortex flow driven by a constant body force is simulated. The numerical setup models the spherical Madison Dynamo Experiment, which uses an impeller-driven flow of liquid sodium. The study focuses on small magnetic Prandtl numbers (Pm), the regime relevant to liquid sodium experimental flows. The critical magnetic Reynolds number (Rm_c) of the dynamo model is determined. It initially rises steeply quasi-linearly as a function of the Reynolds number (Re) by about a factor of 10. Finally, it starts to flatten for Pm ≲ 0.1. Further investigations yield that the initial rise of the stability curve is caused in concert with large- and small-scale fluctuations of the velocity field. As an inertial range of turbulence develops with increasing Re, small-scale dynamo modes become unstable, indicating a transition from large-scale (dipolar) to small-scale dynamo action. It is argued that the flattening of the stability curve is related to a saturation of detrimental large-scale velocity fluctuations, the activation of small-scale dynamo action, and the separation of resistive and viscous cutoff scales for Pm < 1. Moreover, it is shown that only the turbulent fluctuations obtained by subtracting the precomputed mean flow from the dynamically evolving flow can act as a small-scale dynamo.