The scaling of the kinematic boundary layer thickness ${\lambda }_u$ and the friction factor $C_f$ at the top and bottom walls of Rayleigh-Bénard convection is studied by direct numerical simulation (DNS). By a detailed analysis of the friction factor, a new parameterisation for $C_f$ and ${\lambda }_u$ is proposed. The simulations were made of an $L/H=4$ aspect-ratio domain with periodic lateral boundary conditions at $\text{Ra}=\left\{{10}^5,{10}^6,{10}^7,{10}^8\right\}$ and $\text{Pr}=1$. The continuous spectrum, as well as significant forcing due to Reynolds stresses, clearly indicates a turbulent character of the boundary layer, while viscous effects cannot be neglected, judging from the scaling of classical integral boundary layer parameters with Reynolds number. Using a conceptual wind model, we find that the friction factor $C_f$ should scale proportionally to the thermal boundary layer thickness as $C_f\propto {\lambda }_{\Theta }/H$, while the kinetic boundary layer thickness ${\lambda }_u$ scales inversely proportionally to the thermal boundary layer thickness and wind Reynolds number ${\lambda }_u/H\propto {({\lambda }_{\Theta }/H)}^{-1}{\text{Re}}^{-1}$. The predicted trends for $C_f$ and ${\lambda }_u$ are in agreement with DNS results.

• Received 3 September 2007

DOI:https://doi.org/10.1103/PhysRevE.77.036312