NUMERICAL MODELING OF THE GEODYNAMO
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
Summary:
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.
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