Laboratory confirmation of diffusion-free heat transport in rapidly rotating convection
In plain words
In a fluid layer heated from below and spun fast, as in planetary cores and oceans, theory predicts a heat-transport law that does not depend on viscosity or heat diffusion. Simulations now show this law, but whether laboratory flows reach it and how it depends on the fluid are open.
Precise statement
Rotating Rayleigh-Benard convection with Ekman number $\mathrm{Ek}=\nu/(2\Omega H^{2})\to 0$ and supercriticality $\mathrm{Ra}\sim=\mathrm{Ra}\,\mathrm{Ek}^{4/3} >> 1$ ($\Omega\ \text{rotation rate},\ H\ \text{layer height}$). The diffusion-free (geostrophic turbulence) prediction is $\mathrm{Nu} - 1 \sim$ $\mathrm{Ra}\sim$$^{(3/2)}$ at fixed Pr. Determine whether this law holds in laboratory cells with sidewalls and centrifugal effects, its Prandtl-number dependence for Pr from about 0.03 to 7, and the $\mathrm{Ra}\sim$ at which it crosses over to non-rotating convection.
What would settle it
Heat-transport measurements in rotating cells at $\mathrm{Ek} <\sim 10^{-8}$ and $\mathrm{Ra}\sim$ well above onset at several Pr, compared with DNS of the same geometry.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
DNS with no-slip plates and periodic sides at $\mathrm{Pr} = 1$, $\mathrm{Ra}\ \text{up to}\ 3 \times 10^{13}$ and $\mathrm{Ek}\ \text{down to}\ 5 \times 10^{-9}$ show $\mathrm{Nu} - 1 \sim \mathrm{Ra}\sim^{(3/2)}$, with a steeper $\mathrm{Ra}\sim^{3}$ regime at lower $\mathrm{Ra}\sim$ (Song, Shishkina, Zhu, J. Fluid Mech. 2024); laboratory confirmation and the Pr dependence remain open.
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