Movies representing possible flow in the Earth liquid core as studied in the project GRACEFUL
Our group at the Royal Observatory studies the dynamics of fluid layers inside rotating planets and moons. It is very difficult to imagine the kind of complex flows that we deal with. To help us with that, we built a miniature model of a fluid planet in our lab. Rotation is of major importance in the study of planetary fluid dynamics. With our lab planet, we wanted to visualise at least qualitatively how the fluid flow changes when the rotation speed varies in time. We needed our ‘planet’ to be as transparent as possible and we also needed a way to control its rotation with some level of precision.
We set to work building our lab planet using an 14” diameter acrylic globe, the same kind as used for outdoor lighting. We used an aluminium disc as a rotating platform mounted on a spherical ball bearing, all resting on a PVC stand. We still needed a way to control the rotation and that was when we heard about DIYnamics and thought it would be a perfect match for our purpose!
In the past, in order to visualise the currents in fluids, scientists used Kalliroscope fluid, a rheoscopic fluid developed by Paul Matisse in 1966, unfortunately not available anymore. We considered mica powder and other alternatives that ended up being not so great compared to Kalliroscope fluid. However, Daniel Borrero-Echeverry from Willamette University devised an ingenious way  to get the same rheoscopic effect as Kalliroscope, simply using shaving cream! We were able to obtain large quantities of rheoscopic fluid, about 22 Kg (or 48 pounds), which we used to fill the acrylic globe. The technical service from the observatory helped us with the machining of the aluminium disc platform. The globe is simply glued (with RTV) to the aluminium disc. We made a threaded hole through the centre of the disc which we use for filling/draining the globe.
Xe use the motorised lego wheel to drive the rotation via the aluminium disc platform. The lego motor is powerful enough to spin the whole device! Mesmerising flow patterns appear when the spin rate is changed slightly, which we do via the IR remote. In the videos you can hear the motors whirring and change pitch as we slow down or spin up the globe, you can see clearly the shear in the flow caused by the accelerating/decelerating globe surface in contact with the fluid.
If we let the globe spin for a while at a constant rate, the fluid will eventually spin at the same rate as the globe, in sync, with no or very little flow in the interior as indicated by the absence of any patterns in the fluid. This might take 5 to 10 minutes to achieve. If we reduce the speed of the globe just a notch, turbulence will develop straddling the equator, induced by Görtler vortices most likely. However, if the fluid is still not yet spinning in unison with the globe surface, turbulence develops within a very well defined band, which we can see in the videos. We can’t claim we understand all features we see in the flow but we do recognise many, some of the them resembling patterns we see in Jupiter, Saturn (think of the polar hexagon), or the Earth’s atmosphere.
Our lab planet has been a real success during our outreach campaigns, more than we anticipated! We have had already a number of open days here at the Observatory, as well as in the Brussels Planetarium and in 2019 we took the device to the annual open door day at the European Space Agency’s centre in Noordwijk, the Netherlands. During these sessions we engage a general audience and discuss various topics related to fluid dynamics at the planetary scale.
The lab planet is a reality thanks to Antony Trinh, Jeremy Rekier, Santiago Andres Triana, the technical service at the Royal Observatory of Belgium, and of course the DIYnamics team for their brilliant idea!
 Borrero-Echeverry, D., Crowley, C. J., & Riddick, T. P. (2018). Rheoscopic fluids in a post-Kalliroscope world. Physics of Fluids, 30(8), 1–6. https://doi.org/10.1063/1.5045053