N. Schaeffer $^{a}$, P. Cardin $^{a}$
$^{a}$ LGIT, Observatoire de Grenoble, France
Nathanael.Schaeffer@ujf-grenoble.fr
In Grenoble, we are preparing a sodium experiment to study magnetostrophic regimes. The flow in the experiment is produced by differential rotation between two concentric spheres. Without magnetic field, Stewartson has shown that the axisymmetric flow is composed of vertical nested shear layers in the linear regime, but little is known about the non linear destabilisation of these layers. Though, we are performing a numerical study of the destabilization of an internal geostrophic shear layer. A quasi geostrophic (2D) code has been developped and is able to reproduce the main features of the flow, down to small Ekman numbers ($E = 10^{-9}$). We find the expected scaling for the thickness of the Stewartson layer in $E^{1/4}$, but also the asymptotic scalings for the onset of instabilities, and the main features of the resulting Rossby waves. Finite amplitude regime is also studied, and compares well with the results of the full 3D calculations performed at higher Ekman numbers ($E = 10^{-5}$). With the same code, we also reproduced the experiments of Fruh and Read (JFM 1999), in a cylinder, with qualitative agreement. As suggested by them, discrepancies could be due to the presence of an inner layer, which is not resolved in our model, but of non-negligible thickness down to relatively small Ekman numbers, since the thickness ratio of these two layers scales like $E^{1/12}$. Finally we investigate the possibility for this helical flow to be a dynamo.