Effect of slip length on flow dynamics and heat transport in two-dimensional Rayleigh–Bénard convection

Abstract

We report a direct numerical simulation (DNS) study of the heat transport and temperature profiles of the plume ejecting and impacting regions in the two-dimensional turbulent Rayleigh–Bénard (RB) convection with slippery plates and horizontally periodic boundary conditions. The numerical study is conducted in the parameter range of Rayleigh number from to and the slip length b from 0 (NS) to ∞ (FS) for the top and bottom plates. Two distinct flow patterns can be seen depending on b, namely convection roll state and zonal flow, which affect the Nusselt number and the Reynolds number . We show that the zonal flow occurs when the normalised slip length , where is the thermal boundary layer thickness for the no-slip (NS) plates. and increase with increasing , and can reach the optimum before the generation of the zonal flow. It is observed that with the effective scaling exponent for the convection roll state, and for the zonal flow. Furthermore, for the convection roll state, the power-law scaling of the local heat flux is in the plume ejecting region, while in the plume impacting region, for varying slip length . The DNS data with different slippery plates for both plume ejecting and impacting regions agree well with the predicted temperature profiles by Huang et al. (J Fluid Mech. 2022;943:A2).