Induction mechanisms in von Kármán swirling flows of liquid gallium

M. Bourgoin¹ - R. Volk¹ - P. Frick² - S. Khripchenko² - Ph. Odier¹ - J.-F. Pinton¹

¹ Laboratoire de Physique, ENS, 46 allée d'Italie, F-69007, Lyon, France
² Institute of Continuous Media Mechanics, Korolyov 1, 614061 Perm, Russia

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 Kármán 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 Kármán mean flow, i.e. without having to invoke the effects of turbulent fluctuations. Tables 1, Figs 11, Refs 24.