Turbulent magnetohydrodynamic dynamo action in a spherically bounded von Karman 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 less than or similar to 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.