Nathanaël Schaeffer

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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)
Rapidly rotating spherical kinematic dynamos at very low Ekman and Prandtl numbers are computed using the combination of a quasi geostrophic (QG) model for the velocity field and a classical spectral 3D code for the magnetic field. The QG flow is computed in the equatorial plane of the sphere and corresponds to Rossby wave instabilities of a geostrophic(More)
We use a quasi-geostrophic numerical model to study the turbulence of rotating flows in a sphere, with realistic Ekman friction and bulk viscous dissipation. The forcing is caused by the destabilization of an axisymmetric Stewartson shear layer, generated by differential rotation, resulting in a forcing at rather large scales. The equilibrium regime is(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 Pm. In the special case Pm = 1, there is no reflection on an insulating, no-slip boundary, and the(More)
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,(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)