From large-scale to small-scale dynamos in a spherical shell

Kinematic dynamo action in a spherical shell is studied with a small-scale cellular prescribed velocity field. Three velocity fields are considered, all of which are axisymmetric and have a large-scale separation between the shell size and the dominant scale of the motion. The first flow is steady and strongly helical, so that a mean field dynamo might be expected. We find that indeed large-scale dynamo action is obtained at onset, but that the dynamo is of small-scale type at large magnetic Reynolds number R-m, where advection processes dominate and the magnetic field is generated on the scale of the cells in the flow. We study the transition between these two dynamo processes and find a gradual transition as R-m is increased, where the energy is slowly passed from the large scales to the small scales as the two dynamo processes morph into one another. The second flow, a time-dependent version of the first, produces almost identical results, but the transition appears to occur at smaller R-m than in the steady case and there is some evidence of fast dynamo action as R-m becomes large. The third flow, a nonhelical variant of the first flow, is also studied, and small-scale dynamo action was found at onset in this case, with a much larger critical value of R-m for growth of the magnetic field. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4757661]