Optimal Prandtl number for heat transfer in rotating Rayleigh–Bénard convection

Numerical data for the heat transfer as a function of the Prandtl (Pr) and Rossby (Ro) numbers in turbulent rotating Rayleigh–Bénard convection are presented for Rayleigh number Ra = 108. When Ro is fixed, the heat transfer enhancement with respect to the non-rotating value shows a maximum as a function of Pr. This maximum is due to the reduced effect of Ekman pumping when Pr becomes too small or too large. When Pr becomes small, i.e. for large thermal diffusivity, the heat that is carried by the vertical vortices spreads out in the middle of the cell and Ekman pumping thus becomes less effective. For higher Pr the thermal boundary layers (BLs) are thinner than the kinetic BLs and therefore the Ekman vortices do not reach the thermal BL. This means that the fluid that is sucked into the vertical vortices is colder than that for lower Pr, which limits the upwards heat transfer. Turbulent Rayleigh–Bénard (RB) convection, i.e. the flow of a fluid between two parallel plates heated from below and cooled from above, is the paradigmatic system for thermally driven turbulence in a confined space. Considerable progress in understanding the flow dependencies has been achieved in the last two decades, as reviewed in [1, 2]. Here we study the case where the sample is rotated around the vertical axis at an angular velocity, �. That system is relevant 4 Author to whom any correspondence should be addressed. New Journal of Physics 12 (2010) 075005 1367-2630/10/075005+08$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft