Geostrophic turbulence heat transfer scalings in experimental rotating convection*

The buoyancy-driven turbulent flows and the associated heat transfers in planetary and stellar interiors are strongly affected by the rapid rotation of these astrophysical bodies. Asymptotic theories have predicted that in the limit of rapid rotation, characterized by vanishingly small Ekman numbers $E$, the flow should enter a "geostrophic turbulence regime". In this regime, the heat flux (measured by the Nusselt number $Nu$) and the temperature difference (measured by the Rayleigh number $Ra$) obey the scaling law $Nu \sim Ra^{3/2} E^{2}$. This scaling can be obtained with simple theoretical arguments: (i) molecular diffusivities should not play a role and (ii) the heat flux if a function of the ratio of Ra over its threshold value. We present a rotating convection experiment where dyed water is heated from below by means of a powerful spotlight shining through the transparent bottom of the rotating tank. When rotation is increased from zero, temperature measurements indicate that the system transitions from the non-rotating diffusivity-free heat-transfer scaling to the geostrophic turbulence regime of rapidly rotating convection.