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Rotating thermal convection in liquid gallium: multi-modal flow, absent steady columns

Aurnou, J.; Bertin, V.; Grannan, A.; Horn, S.; Vogt, T.


Earth's magnetic field is generated by convective motions in its liquid metal core. In this fluid, the heat diffuses significantly more than momentum and thus, the ratio of these two diffusivities, the Prandtl number Pr, is well below unity. The thermally-driven convective flow dynamics of liquid metals are very different from Pr ~ 1 fluids, like water and those used in current dynamo simulations. In order to characterize rapidly rotating thermal convection in low Pr number fluids, we have performed laboratory experiments in an aspect ratio H/D = 1.94 cylinder using liquid gallium (Pr ~0.025) as the working fluid. The Ekman number, E, which characterizes the effect of rotation, varies from E = 5x10^-5 to 5x10^-6 and the Rayleigh number, Ra, which characterizes the buoyancy forcing, varies from Ra ~ 2x10^5 to 1.5x10^7. Using measurements of heat transfer effciency, characterized by the Nusselt number Nu, and point-wise temperature measurements within the fluid, we characterize the different styles of low Pr rotating convective flow.
The convection threshold is first overcome in the form of container scale inertial oscillatory modes. At stronger forcing, sidewall-attached modes are identifed for the first time in liquid metal laboratory experiments. These wall modes coexist with the bulk oscillatory modes. At Ra well below the values where steady rotating columnar convection occurs, the bulk flow becomes turbulent. Our results imply that rotating convective flows in liquid metals do not develop in the form of quasi-steady columns, as in Pr ~ 1 fluids, but in the form of oscillatory convective motions. Therefore, the flows that drive thermally-driven dynamo action in low Pr geophysical and astrophysical fluids can differ substantively than those occuring in current-day Pr ~ 1 numerical models. Since oscillatory convection is significantly easier to excite than steady convection, it may be that thermally-driven oscillatory motions will generate dynamo action in planetary settings, well before steady convective flows are even actuated. Furthermore, our experimental results show that relatively low wavenumber, wall-attached modes can be dynamically important in rapidly rotating convection in liquid metals.

Keywords: Rayleigh-Benard convection; geodynamo; rotating flows



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