Analysis of the thermal plumes in turbulent Rayleigh–Bénard convection based on well-resolved numerical simulations

Abstract

In this study, direct numerical simulations and high-resolved large eddy simulations of turbulent Rayleigh–Bénard convection were conducted with a fluid of Prandtl number Pr = 0.7 in a long rectangular cell of aspect ratio unity in the cross-section and periodic boundaries in a horizontal longitudinal direction. The analysis of the thermal and kinetic energy spectra suggests that temperature and velocity fields are correlated within the thermal boundary layers and tend to be uncorrelated in the core region of the flow. A tendency of decorrelation of the temperature and velocity fields is also observed for increasing Ra when the flow has become fully turbulent, which is thought to characterize this regime. This argument is also supported by the analysis of the correlation of the turbulent fluctuations |u|′ and θ′. The plume and mixing layer dominated region is found to be separated from the thermal dissipation rates of the bulk and conductive sublayer by the inflection points of the probability density function (PDF). In order to analyse the contributions of bulk, boundary layers and plumes to the mean heat transfer, the thermal dissipation rate PDFs of four different Ra are integrated over these three regions. Hence, it is shown that the core region is dominated by the turbulent fluctuations of the thermal dissipation rate throughout the range of simulated Ra, whereas the contributions from the conductive sublayer due to turbulent fluctuations increase rapidly with Ra. The latter contradicts results by He, Tong & Xia (Phys. Rev. Lett., vol. 98, 2007). The results also show that the plumes and mixing layers are increasingly dominated by the mean gradient contributions. The PDFs of the core region are compared to an analytical scaling law for passive scalar turbulence which is found to be in good agreement with the results of the present study. It is noted that the core region scaling seems to approach the behaviour of a passive scalar as Ra increases, i.e. it changes from pure exponential to a stretched exponential scaling.