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In this paper, we report on very efficient algorithms for the spherical harmonic transform (SHT). Explicitly vectorized variations of the algorithm based on the Gauss-Legendre quadrature are discussed and implemented in the SHTns library which includes scalar and vector transforms. The main breakthrough is to achieve very efficient on-the-fly computations(More)
Alfvén waves propagate in electrically conducting fluids in the presence of a magnetic field. Their reflection properties depend on the ratio between the kinematic viscosity and the magnetic diffusivity of the fluid, also known as the magnetic Prandtl number P m. In the special case P m = 1, there is no reflection on an insulating, no-slip boundary, and the(More)
We present a reconstruction of the mean axisymmetric azimuthal and meridional flows in the Derviche Tourneur Sodium installation in Grenoble liquid sodium experiment. The experimental device sets a spherical Couette flow enclosed between two concentric spherical shells where the inner sphere holds a strong dipolar magnet, which acts as a magnetic propeller(More)
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 Rm≈100 to obtain radial profiles of the α and β effects and maps of the mean flow. It appears(More)
In our Letter, we report on magneto-hydrodynamic turbulence experiments in a spherical cavity filled with liquid sodium and permeated by a strong magnetic field. We find that a negative β effect, which is interpreted as a reduction of the effective magnetic diffusivity [1], best explains our experimental data. In addition, we present direct numerical(More)
Torsional Alfvén waves propagating in the Earth's core have been inferred by inversion techniques applied to geomagnetic models. They appear to propagate across the core but vanish at the equator, exchanging angular momentum between core and mantle. Assuming axial symmetry, we find that an electrically conducting layer at the bottom of the mantle can lead(More)
We present a dynamo mechanism arising from the presence of barotrop-ically unstable zonal jet currents in a rotating spherical shell. The shear instability of the zonal flow develops in the form of a global Rossby mode, whose azimuthal wavenumber depends on the width of the zonal jets. We obtain self-sustained magnetic fields at magnetic Reynolds numbers(More)
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