I will discuss rapidly rotating radiatively driven thermal convection, based on a combination of laboratory experiments and direct numerical simulations (DNS). I will report the simultaneous validation of the scaling predictions of the `geostrophic turbulence' regime - the diffusivity-free or `ultimate' regime of rapidly rotating convection - for the heat transport, the temperature fluctuations, the flow speed and the characteristic horizontal scale. Radiatively driven convection appears as a versatile setup for the laboratory observation of the diffusivity-free regimes of various convective flows of geophysical and/or astrophysical interest.
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