Simulations and theory of mechanically driven, turbulent dynamos in spherical geometry

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The Earth and most of the planets in the solar system, the Sun and other stars, galaxies and galaxy clusters all have magnetic fields which cannot be explained by permanent magnetization. It is generally accepted that these fields are produced by the dynamo effect. In the last few years, remarkable progress has been achieved in validating certain key theoretical concepts via laboratory experiments (e.g., at Riga, Karlsruhe, Maryland, Madison, and Cadarache). Due to the use of liquid sodium, these recent (and ongoing) experiments inevitably involve highly turbulent flows which are expected to play a critical role in the dynamo transition. In order to better understand the nature, role, and control of turbulent flows in mechanically driven, bounded dynamos, we plan to perform numerical simulations with existing, parallel, nonlinear MHD codes, complemented by theoretical investigations. Mainly two type of flows will be studied. Both are in spherical geometry, and both are related to current experiments. One is the flow of two counter-rotating propellers in a stationary spherical vessel, the other is a rotating sphere within a second, concentric, rotating spherical container (spherical Couette flow). One of the central questions to be addressed is the dependence of the critical magnetic Reynolds number on the fluid Reynolds number. The common proposal has the advantage that some fundamental problems with possibly similar solutions can be approached cooperatively.