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

2008

Abstract

The scaling of the kinematic boundary layer thickness u and the friction factor Cf 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 Cf and u 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 C f should scale proportionally to the thermal boundary layer thickness as Cf / H, while the kinetic boundary layer thickness u scales inversely proportionally to the thermal boundary layer thickness and wind Reynolds number u / H / H −1Re−1. The predicted trends for Cf and u are in agreement with DNS results. DOI: 10.1103/PhysRevE.77.036312 PACS number s : 47.20.Bp, 47.27.nb, 44.25. f