Wind and boundary layers in Rayleigh-Bénard convection. II. Boundary layer character and scaling

The scaling of the kinematic boundary layer thickness λᵤ and the friction factor Cf at the top and bottom walls of Rayleigh-B\'enard 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=10⁵,10⁶,10⁷,10⁸ and 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 Cf should scale proportionally to the thermal boundary layer thickness as Cf∝λ_Θ/H, while the kinetic boundary layer thickness λᵤ scales inversely proportionally to the thermal boundary layer thickness and wind Reynolds number λᵤ/H∝(λ_Θ/H)^-1Re^-1. The predicted trends for Cf and λᵤ are in agreement with DNS results.