On the peculiar nature of turbulence in planetary dynamos

Under the combined constraints of rapid rotation, sphericity, and magnetic field, motions in planetary cores get organized in a peculiar way. Classical hydrodynamic turbulence is not present, but turbulent motions can take place under the action of the buoyancy and Laplace forces. Laboratory experiments, such as the rotating spherical magnetic Couette DTS experiment in Grenoble, help us understand what motions take place in planetary core conditions.Comment: in press in Compte Rendu de l'Academie des Science

Etude expérimentale du régime magnétostrophique avec DTS (Derviche Tourneur Sodium)

The DTS (Derviche Tourneur Sodium) experiment has been constructed in order to explore the magnetostrophic regime expected for planetary cores, in which the Coriolis and Lorentz forces are in balance. Two concentric spheres are differentially rotating, and the spherical shell is filled with liquid sodium. A dipolar magnetic field is imposed thanks to permanent magnets inside the inner sphere. This magnetohydrodynamical spherical Couette flow is studied with different measurements : velocity (Doppler), electric potential and induced magnetic field.Angular velocity profiles reveal different regions in the spherical shell : super-rotation is present near the inner sphere, then the angular velocity is nearly constant and decreases towards the outer sphere. The similar shape of angular velocity profiles in the geostrophic region is explained with a model based on a modified Taylor's state, in which the turbulent friction in Ekman layers is considered. In the volume, the level of turbulence is low, and the observed fluctuations are attributed to waves.The scattering for a given forcing could be due to variations in the electric coupling between liquid sodium and the copper inner sphere. Using the electric potential difference as a proxy of the flow velocity, we identify a particular regime from the induced magnetic field measurements. Large amplitudes are obtained for counter-rotating spheres. We suggest that dynamo action might be favored in such a situation.Recent experiments with a good electric coupling yield stable and impressive measurements. Moreover, new induced magnetic field measurements along a meridian and inside the spherical shell give us new constraints.L'expérience DTS (Derviche Tourneur Sodium) permet d'étudier le régime magnétostrophique attendu dans les noyaux planétaires, où les forces de Coriolis et de Lorentz sont en équilibre. Elle consiste en la rotation différentielle de deux sphères concentriques dont l'espace inter-sphère contient du sodium liquide. De plus, un champ magnétique dipolaire est imposé avec une graine aimantée. Cet écoulement magnétohydrodynamique de Couette sphérique est analysé grâce à des mesures de vitesse (Doppler ultrasonore), de potentiel électrique et de champ magnétique induit.Les profils de vitesse angulaire mettent en évidence différentes régions dans le fluide : une zone de super-rotation près de la graine, un plateau, et une décroissance lente à la sphère externe. Ceci est bien expliqué par un modèle basé sur l'état de Taylor modifié où la turbulence dans les couches d'Ekman est prise en compte. Quant à la turbulence dans le volume, elle est faible, et les fluctuations observées sont associées à des ondes.La dispersion des mesures pour un forçage donné pourrait être due à des variations de couplage électrique entre le sodium liquide et la graine en cuivre. L'utilisation de la différence de potentiels électriques, comme équivalent de la vitesse du fluide, amène la découverte d'un régime particulier quand les sphères sont contra-rotatives. Les fortes amplitudes du champ magnétique induit nous laissent penser que cette situation pourrait être favorable à l'obtention d'un effet dynamo.Les récentes expériences ont montré un bon couplage électrique, et des mesures innovantes de champ induit, tout le long d'un méridien et à l'intérieur de la sphère, apportent de nouvelles contraintes

Rotating spherical Couette flow in a dipolar magnetic field: Experimental study of magneto-inertial waves

This paper has been accepted for publication in Journal of Fluid Mechanics published by Cambridge University PressInternational audienceThe magnetostrophic regime, in which Lorentz and Coriolis forces are in balance, has been investigated in a rapidly rotating spherical Couette flow experiment. The spherical shell is filled with liquid sodium and permeated by a strong imposed dipolar magnetic field. Azimuthally travelling hydromagnetic waves have been put in evidence through a detailed analysis of electric potential differences measured on the outer sphere, and their properties have been determined. Several types of waves have been identified depending on the relative rotation rates of the inner and outer spheres: they differ by their dispersion relation and by their selection of azimuthal wavenumbers. In addition, these waves constitute the largest contribution to the observed fluctuations, and all of them travel in the retrograde direction in the frame of reference bound to the fluid. We identify these waves as magneto-inertial waves by virtue of the close proximity of the magnetic and inertial characteristic time scales of relevance in our experiment