Magnetohydrodynamics measurements in the von Kármán sodium experiment

Abstract

We study the magnetic induction in a confined swirling flow of liquid sodium, at integral magnetic Reynolds numbers up to 50. More precisely, we measure in situ the magnetic field induced by the flow motion in the presence of a weak external field. Because of the very small value of the magnetic Prandtl number of all liquid metals, flows with even modest $R_m$ are strongly turbulent. Large mean induction effects are observed over a fluctuating background. As expected from the von Kármán flow geometry, the induction is strongly anisotropic. The main contributions are the generation of an azimuthal induced field when the applied field is in the axial direction (an Ω effect) and the generation of axial induced field when the applied field is the transverse direction (as in a large scale α effect). Strong fluctuations of the induced field, due to the flow nonstationarity, occur over time scales slower than the flow forcing frequency. In the spectral domain, they display a $f^{\text{−1}}$ spectral slope. At smaller scales (and larger frequencies) the turbulent fluctuations are in agreement with a Kolmogorov modeling of passive vector dynamics.