Wind and boundary layers in Rayleigh-Bénard convection. I. Analysis and modeling

Maarten van Reeuwijk, Harm J. J. Jonker, Kemo Hanjalić

Physical Review E · 2008

Abstract

The aim of this paper is to contribute to the understanding of and to model the processes controlling the amplitude of the wind of Rayleigh-Bénard convection. We analyze results from direct simulation of an L / H =4 aspect-ratio domain with periodic sidewalls at Ra= 105 ,106 ,107 ,108 and at Pr=1 by decomposing inde- pendent realizations into wind and fluctuations. It is shown that, deep inside the thermal boundary layer, horizontal heat fluxes exceed the average vertical heat flux by a factor of 3 due to the interaction between the wind and the mean temperature field. These large horizontal heat fluxes are responsible for spatial temperature differences that drive the wind by creating pressure gradients. The wall fluxes and turbulent mixing in the bulk provide damping. Using the direct numerical simulation results to parametrize the unclosed terms, a simple model capturing the essential processes governing the wind structure is derived. The model consists of two coupled differential equations for wind velocity and temperature amplitude. The equations indicate that the formation of a wind structure is inevitable due to the positive feedback resulting from the interaction between the wind and temperature field. Furthermore, the wind velocity is largely determined by the turbulence in the bulk rather than by the wall-shear stress. The model reproduces the Ra dependence of wind Reynolds number and temperature amplitude. DOI: 10.1103/PhysRevE.77.036311 PACS number s : 47.20.Bp, 47.27.nb, 44.25. f