Numerical simulations of rotating Rayleigh-Bénard convection

The Rayleigh-Bénard (RB) system is relevant to astro- and geophysical phenomena, including convection in the ocean, the Earth’s outer core, and the outer layer of the Sun. The dimensionless heat transfer (the Nusselt number Nu) in the system depends on the Rayleigh number Ra=ßg¿L 3/(¿¿) and the Prandtl number Pr=¿/¿. Here, ß is the thermal expansion coefficient, g the gravitational acceleration, ¿ the temperature difference between the bottom and top, and ¿ and ¿ the kinematic viscosity and the thermal diffusivity, respectively. The rotation rate H is used in the form of the Rossby number Ro=(ßg¿/L)/(2H). The key question is: How does the heat transfer depend on rotation and the other two control parameters: Nu(Ra, Pr, Ro)? Here we will answer this question by giving a summary of our result