Low magnetic Prandtl number dynamos

Dynamo amplification by velocity fields in conducting fluids can be highly varied. Here [1] we study dynamos numerically in one of the most efficient flows found for exciting dynamo fields at low magnetic Reynolds numbers: ``Roberts flow,'' in which the large scales are driven helically in 3D periodic boundary conditions. Three qualitatively distinct regimes are identified, depending upon mechanical Reynolds number: steady-state laminar flow, mildly unstable periodic hydrodynamic flow, and fully turbulent hydrodynamic flow. A critical magnetic Reynolds number for dynamo amplification can be identified in all three regimes, and it plateaus as the inverse magnetic Prandtl number increases (paralleling earlier results for the ``Taylor-Green vortex'' flow). It is over five times higher in the turbulent velocity field regime than it is for the time-averaged flow for that turbulent velocity field. Explorations are carried out both in the linear (``kinematic dynamo'') and nonlinear regimes of incompressible MHD. Periodic boundary conditions appear as an undesirable limitation and we are attempting to dispense with them by a spectral method in which the fields are expanded in Chandrasekhar-Kendall spherical eigenfunctions of the curl. [1] P.D. Mininni and D.C. Montgomery, ``Low magnetic Prandtl number dynamos with helical forcing,'' submitted to Phys. Rev. E (2005). Arxiv: physics/0505192.