Rotating Rayleigh-Bénard convection

How does rotation influence heat transport? Our simulations and experiments show how rotation changes the flow organization and can enhance heat transfer through Ekman pumping. The enhancement depends on the Rayleigh and Prandtl numbers, rotation rate and confinement. At fixed buoyancy forcing, the Rossby number Ro is inversely proportional to the rotation rate.

Later developments

• Rotation and confinement (2022): the sampled cylindrical simulations contain separate heat-transport maxima associated with different vortex states; the sampled map does not establish universal optima.
• Optimal rotation at large Rayleigh numbers (2023): the inverse Rossby number giving the sampled maximum heat transport first increases and then decreases with Rayleigh number, while the maximum enhancement weakens at higher Rayleigh numbers in the studied cases.

Foundational results: Ekman pumping

During my PhD we investigated the influence of rotation by using direct numerical simulations and laboratory experiments in the Turbulence and Vortex Dynamics group in Eindhoven in collaboration with Herman Clercx. In the simulations we solve the incompressible Navier-Stokes and temperature equations with rotation in the Boussinesq approximation in a cylinder. Figure 2 shows that the Nusselt number can increase by up to 20% for the water cases studied. At the same imposed temperature difference, this is also a 20% increase in dimensional heat flux. The enhancement is due to Ekman pumping, which draws hot fluid out of the thermal boundary layer; see figure 1.

Figure 3 shows that the heat transfer enhancement as function of the Prandtl number has an optimum. This suggests that the effect of Ekman pumping is determined by two different mechanisms. We find that in the low Prandtl number regime the effect of Ekman pumping is limited by the larger thermal diffusivity of the fluid. Therefore the heat that is sucked into the vortices spreads out in the middle of the cell and this limits the effect of the process. In the high Prandtl number regime the kinetic boundary layer becomes thicker with respect to the thermal boundary layer. Because the vortices are formed at the edge of the kinetic boundary layer the temperature of fluid that is sucked into the vortices decreases with increasing Prandtl and this limits the effect of Ekman pumping in the high Prandtl number regime. A visualisation of these vortices close to the plates is shown in figure 4.