**The influence of inertia on convection in a rotating spherical shell**

Convective flows in the Earth molten outer core are believed to be the motor for the generation of the Earth magnetic field, often called the Geodynamo. Two different types of buoyancy seem to be the main driving sources for those convective flows. Both are a result of the freezing process of the outer core. The first is based on the super adiabatic temperature gradient in the outer core. The second is of chemical nature and is derived from light elements which emerge at the boundary between the inner and the outer core as a result of the freezing process of the outer core.

But so far it is uncertain if the convective flows in the outer core are dominated by thermal or by chemical buoyancy.

On the molecular level the thermal diffusivity differs significantly from the chemical diffusivity in the outer core. Compositional variations diffuse about 1000 times slower than temperature variations.

This has implication on an important parameter in convection, the Prandtl number, which denotes the ratio of the viscosity and the diffusivity, either thermal or chemical. One can show that the Prandtl number controls the importance of the nonlinear inertia term in the momentum equation in the sense that the importance of mechanical inertia increases with decreasing Prandtl number. Relating to convection in the outer core the Prandtl number ranges from ~0.1, if one assumes thermally driven convection, up to ~100, if compositional driven convection is taken into account. Is the outer core mainly driven by thermal buoyancy, inertia would play an important role in the core dynamics. However convective flows in a primarily compositional driven outer core would react nearly instantaneous on density variations.

To investigate this effect in more detail I study the influence of inertia on convective flows in a rotating spherical shell by means of a numerical model. The main focus lies on the question how inertia affects the spatial structure of convective flows, especially differential rotation and helicity, which are particularly important for the generation of planetary magnetic fields.