Ultimate regime of turbulent thermal convection

5 problems

• Mechanism of boundary-layer turbulence at the onset of ultimate convection

  Open

  The theory of the ultimate regime assumes that the thin layers of fluid next to the plates become turbulent. What triggers this, and whether the turbulent layers have the predicted logarithmic profiles, is not established.

• Prandtl-number dependence of heat transport in the ultimate regime

  Open

  How strongly heat transport depends on the fluid's ratio of viscosity to heat diffusivity, the Prandtl number, in the ultimate regime is unknown. This matters because liquid metals, stellar plasma and water have very different Prandtl numbers.

• Laboratory confirmation of diffusion-free heat transport in rapidly rotating convection

  Partially resolved

  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.

• What sets the Rayleigh number of the transition to ultimate convection?

  Contested

  If the steep heat-transport regime exists, it starts at very different heating strengths in different experiments. What fixes the starting point is unknown.

• Does the ultimate $\mathrm{Nu} \sim \mathrm{Ra}^{1/2}$ regime exist in Rayleigh-Benard convection?

  Contested

  When heating from below is strong enough, theory predicts that heat transport should grow as the square root of the heating strength, much faster than at moderate heating. Laboratories using different fluids and cells disagree on whether this 'ultimate' regime has been observed.