Thermal dissipation field and its statistical properties in turbulent Rayleigh-Bénard convection

2009 ◽  
Author(s):  
Xiaozhou He
Keyword(s):  
Statistical Properties ◽  
Thermal Dissipation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

APPROXIMATION OF THE STATIONARY STATISTICAL PROPERTIES OF THE DYNAMICAL SYSTEM GENERATED BY THE TWO-DIMENSIONAL RAYLEIGH–BÉNARD CONVECTION PROBLEM

2011 ◽  
Vol 09 (04) ◽  
pp. 421-446 ◽  
Author(s):  
FLORENTINA TONE ◽  
XIAOMING WANG
Keyword(s):  
Dynamical System ◽  
Global Attractors ◽  
Statistical Properties ◽  
Two Dimensional ◽  
Time Step ◽  
Bénard Convection ◽  
Benard Convection ◽  
Convection Problem ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In this article, we consider a temporal linear semi-implicit approximation of the two-dimensional Rayleigh–Bénard convection problem. We prove that the stationary statistical properties as well as the global attractors of this linear semi-implicit scheme converge to those of the 2D Rayleigh–Bénard problem as the time step approaches zero.

Test of the anomalous scaling of passive temperature fluctuations in turbulent Rayleigh–Bénard convection with spatial inhomogeneity

2014 ◽  
Vol 753 ◽  
pp. 104-130 ◽  
Author(s):  
Xiaozhou He ◽  
Xiao-dong Shang ◽  
Penger Tong
Keyword(s):  
Structure Function ◽  
Temperature Fluctuations ◽  
Thermal Dissipation ◽  
Temperature Structure ◽  
Anomalous Scaling ◽  
Bénard Convection ◽  
Benard Convection ◽  
Turbulent Statistics ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractThe scaling properties of the temperature structure function (SF) and temperature–velocity cross-structure function (CSF) are investigated in turbulent Rayleigh–Bénard convection (RBC). The measured SFs and CSFs exhibit good scaling in space and time and the resulting SF and CSF exponents are obtained both at the centre of the convection cell and near the sidewall. A universal relationship between the CSF exponent and the thermal dissipation exponent is found, confirming that the anomalous scaling of passive temperature fluctuations in turbulent RBC is indeed caused by the spatial intermittency of the thermal dissipation field. It is also found that the difference in the functional form of the measured SF and CSF exponents at the two different locations in the cell is caused by the change of the geometry of the most dissipative structures in the (inhomogeneous) temperature field from being sheetlike at the cell centre to filament-like near the sidewall. The experiment thus provides direct evidence showing that the universality features of turbulent cascade are linked to the degree of anisotropy and inhomogeneity of turbulent statistics.

scholarly journals Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection

2010 ◽  
Vol 643 ◽  
pp. 495-507 ◽  
Author(s):  
RICHARD J. A. M. STEVENS ◽  
ROBERTO VERZICCO ◽  
DETLEF LOHSE
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Layer Structure ◽  
Three Dimensional ◽  
Thermal Dissipation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Boundary Layer Profile

Results from direct numerical simulation (DNS) for three-dimensional Rayleigh–Bénard convection in a cylindrical cell of aspect ratio 1/2 and Prandtl number Pr=0.7 are presented. They span five decades of Rayleigh number Ra from 2 × 106 to 2 × 1011. The results are in good agreement with the experimental data of Niemela et al. (Nature, vol. 404, 2000, p. 837). Previous DNS results from Amati et al. (Phys. Fluids, vol. 17, 2005, paper no. 121701) showed a heat transfer that was up to 30% higher than the experimental values. The simulations presented in this paper are performed with a much higher resolution to properly resolve the plume dynamics. We find that in under-resolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the better-resolved ones, because of insufficient thermal dissipation mainly close to the sidewall (where the grid cells are largest), and therefore the Nusselt number in under-resolved simulations is overestimated. Furthermore, we compare the best resolved thermal boundary layer profile with the Prandtl–Blasius profile. We find that the boundary layer profile is closer to the Prandtl–Blasius profile at the cylinder axis than close to the sidewall, because of rising plumes close to the sidewall.

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