Favier, B. & Proctor, M. R. E. (2013). Kinematic dynamo action in square and hexagonal patterns. Physical Review E (PRE), 88(053011), doi: 10.1103/PhysRevE.88.053011

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Abstract
We consider kinematic dynamo action in rapidly rotating Boussinesq convection just above onset. The velocity is constrained to have either a square or a hexagonal pattern. For the square pattern, largescale dynamo action is observed at onset, with most of the magnetic energy being contained in the horizontally averaged component. As the magnetic Reynolds number increases, smallscale dynamo action becomes possible, reducing the overall growth rate of the dynamo. For the hexagonal pattern, the breaking of symmetry between up and down flows results in an effective pumping velocity. For intermediate rotation rates, this additional effect can prevent the growth of any meanfield dynamo, so that only a smallscale dynamo is eventually possible at large enough magnetic Reynolds number. For very large rotation rates, this pumping term becomes negligible, and the dynamo properties of square and hexagonal patterns are qualitatively similar. These results hold for both perfectly conducting and infinite magnetic permeability boundary conditions.
Item Type:  Article 

Subjects:  Q Science > QC Physics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/2986 
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