During my thesis I concentrated on four different aspects of physics and magnetohydrodynamics taking place in the Earth's core. Each study is presented independently in my dissertation. The first two parts are experimental studies and the two last parts theoretical and numerical calculations. ln the first part, we study experimentally a vertical vortex of liquid metal (gallium) subject to a transverse magnetic field. We investigate the simultaneous effect of Coriolis forces (due to rotation) and Lorentz forces (due to magnetic field ) on a dynamical structure similar to those possibly present in the liquid outer core (convective geostrophic columns). Experimental measurements (fluid velocity, induced magnetic field , differences in electrical potential, temperature) are interpreted with a model providing a clear picture of t he dynamics of the vortex, as weil as a description of the electrical currents generated in the vortex. Coriolis forces tends to rigidify the fluid flow along the rotation axis whereas the main effect of the magnetic field is firstly, to severely slow down the fluid and , secondly, to increase the central part of the vortex. This increase supports the presence of large diameter convective columns in the liquid core. Experimental measurements of ohmic dissipation (Joule heating) demonstrated that large scale toroidal magnetic field in the Earth's core can not exceed 25 mT if the convective flow takes place under geostrophic columns. In the second part, we present an experiment where liquid gallium is crystallized. The goal is to understand the origin of the inner core elastic anisotropy. Experimentally, we observed the crystallization velocities and analyzed the gallium crystal texture. Elastic anisotropy measured within gallium polycrystals (ultrasonic method) showed that crystals axis orientations are not determined by heat flux direction but seemingly by initial germs orientation . Moreover, we showed that gallium texture is independent of solidification conditions such as the vigor of the fluid flow or the imposed magnetic field . We concluded that the inner core anisotropy may be due to a preferred lattice orientation, the orientation being determined by initial germs present in the center of the core. In the third part, we investigate electromagnetic coupling between the liquid outer core and the solid inner core; this study is motivated by recent seismological studies which have endeavoured to observe a differential rotation between the inner core and the mantle. Our numerical simulations show that electromagnetic coupling is extremely efficient between the solid and the liquid: the torque tightly couples the inner core rotation to the fluid motion. Under our assumptions, a relation is established between the outer core toroidal magnetic field and the inner core superrotation. This relationship suggests that a precise determination of the inner core differential rotation might provide a good way to estimate the Earth 's core toroidal magnetic field intensity. In the fourth part we investigate electromagnetic coupling between the liquid core and the solid mantle; we study the influence of an heterogeneous D"-layer (in electrical conductivity) at the base of the mantle on dipole magnetic field pole paths during reversaIs. Heterogeneous electromagnetic coupling results in a differential rotation between the core and the mantle; the rotation is nevertheless very slow (at the time scale of reversais) and can not explain longitudinal confinements of Virtual Geomagnetic Poles (VGP) during reversaIs of the Earth's magnetic field .
Approches experimentales et theoriques de la dynamique du noyau terrestre : tourbillon geostrophique de gallium liquide dans un champ magnetique, anisotropie et rotation de la graine, chemins d'inversion