Heat transport enhancement by rotating bottom endwall in a cylindrical Rayleigh–Bénard convection

Abstract

Rotating thermal convection, commonly encountered in natural and industrial environments, is typically influenced by both buoyancy forces and boundary rotation. In this study, we conduct direct numerical simulations to explore the effect of rotating bottom on the flow structure and heat transport of Rayleigh–Bénard convection (RBC) in a cylindrical cavity. This cavity has a radius-to-height ratio of 1 and is filled with an incompressible fluid with a Prandtl number of 0.7. Our results show that the axisymmetric convection pattern, observed in RBC for Ra∈[4000,8000] without rotation, transitions into a double roll structure at low rotating speeds (ω), while for Ra≤4000, the pattern remains axisymmetric, independent of ω. We then focus on the impact of bottom rotation on heat transport in the axisymmetric regime. Based on the variation in the Nusselt number (Nu) with ω, two distinct regimes are identified: a convection-dominated regime at low ω, where Nu closely resembles that of standard RBC, and a rotation-dominated regime at high ω, where strong shear induced by the rotating bottom intensifies the meridional circulation, significantly boosting global heat flux. The critical rotating speed, ω*, marking the transition between these regimes, follows different power-law relations below and above the buoyant convection onset (Rac): ω*∼Ra−0.64 for Ra<Rac and ω*∼Ra0.33 for Ra>Rac. As ω increases, the exponents for Nu∼Raλ and Re∼Raγ evolve before converging to λ≈0.3 and γ=0.5, respectively. Scaling laws for Nu and Re as functions of ω and Ra in the rotation-dominated regime are finally derived: Nu∼Ra0.3ω0.64 and Re∼Ra0.5ω.