Wind and boundary layers in Rayleigh-Bénard convection. II. Boundary layer character and scaling
Abstract
The scaling of the kinematic boundary layer thickness λu 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 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∝λΘ/H , while the kinetic boundary layer thickness λu scales inversely proportionally to the thermal boundary layer thickness and wind Reynolds number λu/H∝(λΘ/H)-1Re-1 . The predicted trends for Cf and λu are in agreement with DNS results.
- Publication:
-
Physical Review E
- Pub Date:
- March 2008
- DOI:
- 10.1103/PhysRevE.77.036312
- arXiv:
- arXiv:0709.1891
- Bibcode:
- 2008PhRvE..77c6312V
- Keywords:
-
- 47.20.Bp;
- 47.27.nb;
- 44.25.+f;
- Buoyancy-driven instabilities;
- Boundary layer turbulence;
- Natural convection;
- Physics - Fluid Dynamics
- E-Print:
- Phys. Rev. E 77, 036312 2008