The geoflow-experiment on ISS (Part II): Numerical simulation

Abstract

Convection in spherical shells under the influence of a radial force field is an important problem in classical convection theory. It is difficult to reproduce in a terrestrial laboratory though, because there gravity is everywhere downwards rather than radially inwards. It turns out that one can produce a radial force field, by applying a high voltage difference between the inner and outer spheres. The combination of the electric field and the temperature-dependence of the fluid's dielectric coefficient then produces an r −5 central force field. Of course, in a terrestrial laboratory one still has the external gravity as well. In order to eliminate this effect and produce a purely radial force field, an experiment is planned on the International Space Station. In this paper we will present the results of numerical simulations intended to assist in the design of this experiment, for example in choosing the optimal radius ratios. We solve for the onset of convection in such an r −5 force field, as a function of the radius ratio (varying between 0.3 and 0.6), the Prandtl number (varying between 1 and 100), and the Taylor number (measuring an overall rotation of the whole shell, which will also be possible in the experiment).