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To provide insights into the challenging problem of turbulent convection, Jack Herring used a greatly truncated version of the complete Boussinesq equations containing only one horizontal wavenumber. In light of later observations of a robust large scale circulation sweeping through convecting enclosures at high Rayleigh numbers, it is perhaps not an implausible point of view from which to reexamine high-Rayleigh-number data. Here we compare past experimental data on convective heat transport at high Rayleigh numbers with predictions from Herring's model and, in fact, find excellent agreement. The model has only one unknown parameter compared to the two free parameters present in the lowest order least-squares power-law fit. We discuss why the underlying simplistic physical picture, meant to work at Rayleigh numbers slightly past the critical value of a few thousands, is consistent with the data, when the single free parameter in it is revised, over some eleven decades of the Rayleigh number -- stretching from about a million to about $10^{17}$.

We report experimental measurements of heat transport in rotating Rayleigh-B{\'e}nard convection in a cylindrical convection cell with aspect ratio $\Gamma = 1/2$. The fluid was helium gas with Prandtl number Pr = 0.7. The range of control parameters was Rayleigh number $4 \times 10^9 < {\rm Ra} < 4 \times 10^{11}$ and Ekman number $2 \times 10^{-7} < {\rm Ek} < 3 \times 10^{-5}$(corresponding to Taylor number $4 \times 10^9 < {\rm Ta} < 1 \times 10^{14}$ and convective Rossby number $0.07 < {\rm Ro} < 5$). We determine the crossover from weakly rotating turbulent convection to rotation dominated geostrophic convection through experimental measurements of the normalized heat transport Nu. The heat transport for the rotating state in the geostrophic regime, normalized by the zero-rotation heat transport, is consistent with scaling of $({\rm RaEk}^{-7/4})^\beta$ with $\beta \approx 1$. A phase diagram is presented that encapsulates measurements on the potential geostrophic turbulence regime of rotating thermal convection., Comment: 4 pages, 4 figures