Emmanuel Dormy

A thesis submitted in the fulfilment of

the requirements for the degree of

Doctor of Philosophy

Institut de Physique du Globe de Paris

November 1997


We are interested in determining to what extent numerical investigations can help our understanding of the geodynamo. To do so, we perform studies of simplified problems and try to describe with care the different equilibria corresponding to different parameter ranges. We show that overestimating the Ekman number (which is the ratio of viscous to Coriolis forces) can lead to equilibria irrelevent for the Earth's core dynamics and thus to behavior qualitatively very different from that expected in the asymptotic limit of small Ekman numbers. Firstly, we consider an axisymmetrical, laminar problem, for which all motions are driven by a differential rotation of the two bounding spheres. We obtain the agreement between numerical simulations and analytical work for Ekman numbers smaller than 10-6. Secondly, we investigate the magnetohydrodynamic flow with an imposed dipolar field. It is shown that the magnetic effects do not lower the importance of viscous effects on the flow. On the contrary, a magnetoviscous equilibrium can be constructed. Finally we study, in the same geometry, thermal convection as a preliminary step to dynamo action. We describe, with realistic boundary conditions, the convective bifurcation, first at onset and then in finite amplitude. Our study indicates that the disagreement between numerical observation of super-critical bifurcation and theoritical demonstration of sub-critical bifurcation relies in the use of over estimated Ekman numbers in numerical simulations. This points out that convection, as it has been numerically investigated, does not give non-linear terms the same important role as in the asymptotic limit relevant to the Earth's core.

Full thesis manuscript (in french).

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