Boundary Layer Scaling in Rayleigh-bénard Convection

The scaling of the kinematic boundary layer thickness λu and the friction factor Cf at the topand bottom-wall of Rayleigh-Bénard convection is studied by Direct Numerical Simulation (DNS). By a detailed analysis of the friction factor, a new parameterisation for Cf and λu is proposed. The simulations were made of an L/H = 4 aspect-ratio domain with periodic lateral boundary conditions at Ra = {105, 10, 107} and Pr = 1. The best-fits of the simulations are λu ∝ Ra−0.13 and Cf ∝ Ra−0.3. By analysing the horizontal momentum equation, it is shown that the friction factor is dominated by the pressure gradient. Using a conceptual wind model, we find that the friction factor Cf should scale proportional to the thermal boundary layer thickness as Cf ∝ λΘ, while the kinetic boundary layer thickness λu scales inversely proportional to the thermal boundary layer thickness and wind Reynolds number λu ∝ λ−1 Θ Re−1. The predicted trends for Cf and λu are in agreement with DNS results.