Measurements of the local thermal dissipation rate in turbulent Rayleigh-Bénard convection

2005 ◽  
Author(s):  
Xiaozhou He
Keyword(s):  
Dissipation Rate ◽  
Thermal Dissipation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

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 A Lagrangian fluctuation–dissipation relation for scalar turbulence. Part III. Turbulent Rayleigh–Bénard convection

2017 ◽  
Vol 836 ◽  
pp. 560-598
Author(s):  
Gregory L. Eyink ◽  
Theodore D. Drivas
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Dissipation Rate ◽  
Mixing Time ◽  
Thermal Dissipation ◽  
Fluctuation Dissipation ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Near Wall

A Lagrangian fluctuation–dissipation relation has been derived in a previous work to describe the dissipation rate of advected scalars, both passive and active, in wall-bounded flows. We apply this relation here to develop a Lagrangian description of thermal dissipation in turbulent Rayleigh–Bénard convection in a right-cylindrical cell of arbitrary cross-section, with either imposed temperature difference or imposed heat flux at the top and bottom walls. We obtain an exact relation between the steady-state thermal dissipation rate and the time $\unicode[STIX]{x1D70F}_{mix}$ for passive tracer particles released at the top or bottom wall to mix to their final uniform value near those walls. We show that an ‘ultimate regime’ with the Nusselt number scaling predicted by Spiegel (Annu. Rev. Astron., vol. 9, 1971, p. 323) or, with a log correction, by Kraichnan (Phys. Fluids, vol. 5 (11), 1962, pp. 1374–1389) will occur at high Rayleigh numbers, unless this near-wall mixing time is asymptotically much longer than the free-fall time $\unicode[STIX]{x1D70F}_{free}$. Precisely, we show that $\unicode[STIX]{x1D70F}_{mix}/\unicode[STIX]{x1D70F}_{free}=(RaPr)^{1/2}/Nu,$ with $Ra$ the Rayleigh number, $Pr$ the Prandtl number, and $Nu$ the Nusselt number. We suggest a new criterion for an ultimate regime in terms of transition to turbulence of a thermal ‘mixing zone’, which is much wider than the standard thermal boundary layer. Kraichnan–Spiegel scaling may, however, not hold if the intensity and volume of thermal plumes decrease sufficiently rapidly with increasing Rayleigh number. To help resolve this issue, we suggest a program to measure the near-wall mixing time $\unicode[STIX]{x1D70F}_{mix}$, which is precisely defined in the paper and which we argue is accessible both by laboratory experiment and by numerical simulation.

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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