Abstract
Using in situ magnetic field measurements, we study the induction mechanisms in a swirling flow of liquid Gallium generated inside a cylinder, in the gap between two coaxial rotating discs. The von Karman flow generated in this manner has both helicity and differential rotation. Magnetic Reynolds numbers Rm up to 7 (based on the disc rim speed) are generated. We study the magnetic induction when an external field is applied successively along the axis, in the azimuthal direction or tranverse to the axis of rotation. In the first two cases, both the flow and the magnetic field are axisymmetric, and an effective mechanism of conversion from poloidal to toroidal field exists but, in agreement with Cowling's theorem, no reciprocal mechanism can be identified. When the applied magnetic field is transverse to the flow, the axial symmetry is broken and several non-axysimmetric mechanisms can generate an axial field from the applied transverse one: a linear (in Rm) induction by the radial gradients of the poloidal flow; a quadratic (in Rm), Parker-like, induction by the flow helicity and an effect entirely due to the discontinuity of electrical conductivity at the boundary of the flow. In all of our observations, the mean induction can be explained using the topology of the von Karman mean flow, i.e. without having to invoke the effects of turbulent fluctuations.
Highlights
A complex flow of an electrically conducting fluid can under some conditions generate a large-scale magnetic field [1,2,3]
Using in situ magnetic field measurements, we study the induction mechanisms in a swirling flow of liquid Gallium generated inside a cylinder, in the gap between two coaxial rotating discs
The second element of the dynamo cycle is more subtle: it cannot be achieved by a laminar axisymmetric flow (Cowling’s theorem), but it can exist if the axial symmetry is broken at smaller scales, if the subscale motion is helical
Summary
A complex flow of an electrically conducting fluid can under some conditions generate a large-scale magnetic field [1,2,3] This phenomenon is called the magnetohydrodynamic (MHD) dynamo. The second element of the dynamo cycle is more subtle: it cannot be achieved by a laminar axisymmetric flow (Cowling’s theorem), but it can exist if the axial symmetry is broken at smaller scales, if the subscale motion is helical. This process is at the heart of the Roberts dynamo [5], which underlies the Karlsruhe experiment [6]. Self-generation of a non-stationary dynamo magnetic field is possible from a single helical flow, as analytically proposed by Ponomarenko [7] and experimentally demonstrated in the Riga experiment [8]
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