| Several teams have reported peculiar frequency spectra for flows in a spherical shell. To address their origin, we perform numerical simulations of the spherical Couette flow in a dipolar magnetic field, in the configuration of the DTS experiment. The frequency spectra computed from time-series of the induced magnetic field display similar bumpy spectra, where each bump corresponds to a given azimuthal wave number m. The bumps show up at moderate Reynolds number (2 600) if the time-series are long enough (300 rotations of the inner sphere). We present a new method that permits to retrieve the dominant frequencies for individual wave numbers m, and to extract the non-linear modal structure of the flow. The maps of the energy of the fluctuations and the spatio-temporal evolution of the velocity field suggest that fluctuations originate in the outer boundary layer. Comparisons with the linear stability analysis of this Bödewadt layer confirm this hypothesis. We explore the variation of the magnetic and kinetic energies with the input parameters, and show that a modified Elsasser number controls their evolution. We can thus compare with experimental determinations of these energies and find a good agreement. Because of the dipolar nature of the imposed magnetic field, the energy of magnetic fluctuations is much larger near the inner sphere, but their origin lies in velocity fluctuations that initiate in the outer boundary layer. Our results suggest that the contribution of boundary layer instabilities to turbulence in the Earth's liquid core could have been underestimated. |
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