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

• Published in: Physics of fluids (1994) 2012-10, Vol.24 (10)
• Main Authors: RICHARDSON, K. J, HOLLERBACH, R, PROCTOR, M. R. E
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fluid dynamics; Fluid flow; Fundamental areas of phenomenology (including applications); Helical; Magnetic fields; Magnetohydrodynamics and electrohydrodynamics; Physics; Rotating generators; Shells; Small scale; Spherical shells
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.4757661

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 Rm, 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 Rm 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 Rm than in the steady case and there is some evidence of fast dynamo action as Rm 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 Rm for growth of the magnetic field.