Magnetic induction maps in a magnetized spherical Couette flow experiment

The DTS experiment is a spherical Couette flow experiment with an imposed dipolar magnetic field. Liquid sodium is used as a working fluid. In a series of measurement campaigns, we have obtained data on the mean axisymmetric velocity, the mean induced magnetic field and electric potentials. All these quantities are coupled through the induction equation. In particular, a strong ω-effect is produced by differential rotation within the fluid shell, inducing a significant azimuthal magnetic field. Taking advantage of the simple spherical geometry of the experiment, I expand the azimuthal and meridional fields into Legendre polynomials and derive the expressions that relate all measurements to the radial functions of the velocity field for each harmonic degree. For small magnetic Reynolds numbers Rm the relations are linear, and the azimuthal and meridional equations decouple. Selecting a set of measurements for a given rotation frequency of the inner sphere ( Rm ≃ 9.4 ), I invert simultaneously the velocity and the magnetic data and thus reconstruct both the azimuthal and the meridional fields within the fluid shell. The results demonstrate the good internal consistency of the measurements, and indicate that turbulent non-axisymmetric fluctuations do not contribute significantly to the axisymmetric magnetic induction.