Turbulence Reduces Magnetic Diffusivity in a Liquid Sodium Experiment

The contribution of small scale turbulent fluctuations to the induction of a mean magnetic field is investigated in our liquid sodium spherical Couette experiment with an imposed magnetic field. An inversion technique is applied to a large number of measurements at $\mathrm{Rm}\approx 100$ to obtain radial profiles of the $\alpha$ and $\beta$ effects and maps of the mean flow. It appears that the small scale turbulent fluctuations can be modeled as a strong contribution to the magnetic diffusivity that is negative in the interior region and positive close to the outer shell. Direct numerical simulations of our experiment support these results. The lowering of the effective magnetic diffusivity by small scale fluctuations implies that turbulence can actually help to achieve self-generation of large scale magnetic fields.

Figure 1

Sketch of the DTS experiment with its liquid sodium contained between an outer stainless steel shell (gray, with latitude labels in degrees) and an inner copper sphere (orange), which spins as indicated by the red arrow around the vertical rotation axis (here tilted for clarity). Left half of the sphere: the field lines of the dipolar magnetic field imposed by the central magnet are drawn on top of the contour map of the fluid angular velocity $\omega$ (normalized by that of the inner sphere) inverted from data measured for $\mathrm{Rm}=94$. Right half of the sphere: field lines of the total reconstructed magnetic field. The field lines are strongly distorted by the flow ($\omega$ effect). The blue cones mark the radial positions of the six magnetometers $P1$ ($r=\text{radius}/r_o=0.99$) to $P6$ ($r=0.50$), which measure the azimuthal magnetic field. They can be placed at four different latitudes (here $-20°$).

Figure 2

Radial profiles of the $\alpha$ effect (a) and $\beta$ effect (b) with their error bars, obtained by the inversion of DTS data for two magnetic Reynolds numbers: $\mathrm{Rm}=28$ and 72. The a priori null profile, along with its error bar, is also drawn. The blue curve shows the $\alpha (r)$ and $\beta (r)$ profiles retrieved from a numerical simulation of the DTS experiment at $\mathrm{Rm}=29$ and $\mathrm{Re}=2.9\times {10}^4$, blown up by a factor $4\times {10}^4$.

Figure 3

Measurements and model fits for an example of time-varying magnetic signals measured at $2f$ ($m=2$) and $3f$ ($m=3$) frequencies, for a rotation rate of the inner sphere $f=-23\mathrm{Hz}$ ($\mathrm{Rm}=72$). See the text for explanations.

Figure 4

Meridional cross section contour maps showing orthoradial component $\theta$ of emf $\mathcal{E}$ and of electrical current $⟨\mathbf{J}⟩$. (a) Averaged emf ${\mathcal{E}}_t$ obtained from DNS. (b) Reconstructed emf ${\mathcal{E}}_{\alpha \beta }$ from inverted $\alpha$ and $\beta$ profiles. High latitudes (white area) are excluded from the least-squares fit. (c) Mean electrical current from DNS.