Prandtl-number dependence of heat transport in turbulent Rayleigh-Bénard convection

We present measurements of the Nusselt number N as a function of the Rayleigh number R and the Prandtl number sigma in cylindrical cells with aspect ratios gamma = 0.5 and 1.0. We used acetone, methanol, ethanol, and 2-propanol with Prandtl numbers sigma = 4.0, 6.5, 14.2, and 34.1, respectively, in the range 3x10(7) less, similarR less, similar10(11). At constant R, N(R,sigma) varies with sigma by only about 2%. This result disagrees with the extrapolation of the Grossmann and Lohse theory beyond its range of validity, which implies a decrease by 20% over our sigma range, but agrees with their recent extension of the theory to small Reynolds numbers.     

Measured local heat transport in turbulent Rayleigh-Bénard convection

Local convective heat flux in turbulent thermal convection is obtained from simultaneous velocity and temperature measurements in an aspect-ratio-one convection cell filled with water. It is found that fluctuations of the vertical heat flux are highly intermittent and are determined primarily by the thermal plumes in the system. The experiment reveals a unique mechanism for the heat transport in turbulent convection.     

Scaling of the local convective heat flux in turbulent Rayleigh-Bénard convection

Local convective heat flux J(r) in turbulent thermal convection is obtained from simultaneous velocity and temperature measurements in a cylindrical cell filled with water. The measured J(r) in the bulk region shows a different scaling behavior with varying Rayleigh numbers compared with that measured in the plume-dominated regions near the sidewall and near the lower conducting plate. The local transport measurements thus allow us to disentangle boundary and bulk contributions to the total heat flux and directly check their respective scaling behavior against the theoretical predictions.     

Wind reversals in turbulent Rayleigh-Bénard convection

The phenomenon of irregular cessation and subsequent reversal of the large-scale circulation in turbulent Rayleigh-Bénard convection is theoretically analyzed. The force and thermal balance on a single plume detached from the thermal boundary layer yields a set of coupled nonlinear equations, whose dynamics is related to the Lorenz equations. For Prandtl and Rayleigh numbers in the range 10(-2) < or = Pr < or = 10(3) and 10(7) < or = Ra < or = 10(12), the model has the following features: (i) chaotic reversals may be exhibited at Ra > or = 10(7); (ii) the Reynolds number based on the root mean square velocity scales as Re(rms) approximately Ra([0.41...0.47]) (depending on Pr), and as Re(rms) approximately Pr(-[0.66...0.76]) (depending on Ra); and (iii) the mean reversal frequency follows an effective scaling law omega/(nu L(-2)) approximately Pr(-(0.64 +/- 0.01))Ra(0.44 +/- 0.01). The phase diagram of the model is sketched, and the observed transitions are discussed.     

New perspectives in turbulent Rayleigh-Bénard convection

Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Bénard convection are presented. Particular emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers. We also discuss important extensions of Rayleigh-Bénard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.     

New perspectives in turbulent Rayleigh-Bénard convection

Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Bénard convection are presented. Particular emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers. We also discuss important extensions of Rayleigh-Bénard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.     

Onset of coherent oscillations in turbulent Rayleigh-Bénard convection

We report temperature cross correlation and velocity profile measurements in the aspect-ratio-one convection cell filled with water. A sharp transition from a random chaotic state to a correlated turbulent state of finite coherence time is found when the Rayleigh number becomes larger than a critical value Ra(c) approximately equal to 5 x 10(7). The experiment reveals a unique mechanism for the onset of coherent oscillations in turbulent Rayleigh-Bénard convection.     

Heat-flux measurement in high-Prandtl-number turbulent Rayleigh-Bénard convection

We report Nusselt number measurements from high Prandtl number turbulent thermal convection experiments. The experiments are conducted in four fluids with the Prandtl number Pr varying from 4 to 1350 and the Rayleigh number Ra from 2x10(7) to 3x10(10), all in a single convection cell of unity aspect ratio. We find that the measured Nusselt number decreased about 20% over the range of Pr spanned in the experiment. The measure data are also found in good agreement with the prediction of a recent theory over the extended range of Pr covered in the experiment.     

Reorientation of the large-scale circulation in turbulent Rayleigh-Bénard convection

We present measurements of the orientation theta0(t) of the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection in cylindrical cells of aspect ratio 1. Theta0(t) undergoes irregular reorientations. It contains reorientation events by rotation through angles delta theta with a monotonically decreasing probability distribution p(delta theta), and by cessations (where the LSC stops temporarily) with a uniform p(delta theta). Reorientations have Poissonian statistics in time. The amplitude of the LSC and the magnitude of the azimuthal rotation rate have a negative correlation.     

Characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection

We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh–Benard convection in′a square cavity by direct numerical simulations.The Rayleigh number range is 1×10⁸≤Ra≤1×10¹³,and the Prandtl number is selected as Pr=0.7 and Pr=4.3.It is found that the temperature fluctuation profiles with respect to Ra exhibit two different distribution patterns.In the thermal boundary layer,the normalized fluctuationθrms/θrms,max is independent of Ra and a power law relation is identified,i.e.,θrms/θrms,max～(z/δ)0.99±0.01,where z/δis a dimensionless distance to the boundary(δis the thickness of thermal boundary layer).Out of the boundary layer,when Ra≤5×10⁹,the profiles ofθrms/θrms,max descend,then ascend,and finally drop dramatically as z/δincreases.While for Ra≥1×10¹⁰,the profiles continuously decrease and finally overlap with each other.The two different characteristics of temperature fluctuations are closely related to the formation of stable large-scale circulations and corner rolls.Besides,there is a critical value of Ra indicating the transition,beyond which the fluctuation hθrmsiV has a power law dependence on Ra,given by hθrmsiV～Ra?0.14±0.01.     

Morphological evolution of thermal plumes in turbulent Rayleigh-Bénard convection

An experimental study of the morphological evolution of thermal plumes in turbulent thermal convection is presented. Individual sheetlike plumes are extracted and their area, circumference, and "heat content" are found to all exhibit log-normal distributions. As the sheetlike plumes move across the plate they collide and convolute into spiraling swirls. These swirls then spiral away from the plates to become mushroomlike plumes which are accompanied by strong vertical vorticity. The measured profiles of plume numbers and of vertical vorticity quantify the morphological transition of sheetlike plumes to mushroomlike ones and the mixing and merging or clustering of mushroomlike plumes. The fluctuating vorticity is found to have the same exponential distribution and scaling behavior as the fluctuating temperature.     

Measured thermal dissipation field in turbulent Rayleigh-Bénard convection

The time-averaged local thermal dissipation rate epsilonN(r) in turbulent convection is obtained from direct measurements of the temperature gradient vector in a cylindrical cell filled with water. It is found that epsilonN(r) contains two contributions. One is generated by thermal plumes, present mainly in the plume-dominated bulk region, and decreases with increasing Rayleigh number Ra. The other contribution comes from the mean temperature gradient, being concentrated in the thermal boundary layers, and increases with Ra. The experiment thus provides a new physical picture about the thermal dissipation field in turbulent convection.     

Large-scale circulation model for turbulent Rayleigh-Bénard convection

A model for the large-scale-circulation (LSC) of turbulent Rayleigh-Bénard convection in cylindrical samples is presented. It consists of two physically motivated stochastic ordinary differential equations, one each for the strength and the azimuthal orientation of the LSC. Stochastic forces represent phenomenologically the influence of turbulent fluctuations. Consistent with measurements, the model yields an azimuthally meandering LSC with occasional rotations, and with more rare cessations. As in experiment, cessations have a uniform distribution of LSC orientation changes.     

Nusselt number measurements for turbulent Rayleigh-Bénard convection

We present high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for a cylindrical sample of water (Prandtl number sigma=4.4) of height L approximately equal to 50 cm and aspect ratio Gamma identical with D/L approximately equal to 1 (D is the diameter) for 3 x 10(9)< or =R< or =6 x 10(10). For R approximately 3 x 10(9) the data are consistent with existing results for acetone (sigma=4.0, R< or =3 x 10(9)). There the measurements are also consistent with a model by Grossmann and Lohse (GL). As R increases, the measurements fall below the GL prediction. Near R=6 x 10(10) the prediction is 8% above the data.     

Plume fragmentation by bulk interactions in turbulent Rayleigh-Bénard convection

Using compressed gases with Prandtl numbers near 0.7, we obtained flow visualizations of turbulent Rayleigh-Bénard convection in a cylindrical sample with an aspect ratio Γ≡D/L?10 (D is the diameter and L the height) by the shadowgraph method. Focusing on the plumes under the top plate, we found that their length had a log-normal distribution, suggesting a fragmentation process. Fragmentation events could be visually identified in the images and involved plume interactions with bulk fluctuations or upwelling domain walls. We found the mean spacing between plumes to vary with the Rayleigh number in proportion to the volume-averaged Kolmogorov length of the turbulent bulk fluctuations, providing further evidence for plume-bulk interactions.     

Transition to the ultimate state of turbulent Rayleigh-Bénard convection

Measurements of the Nusselt number Nu and of a Reynolds number Re(eff) for Rayleigh-Bénard convection (RBC) over the Rayleigh-number range 10(12)?Ra?10(15) and for Prandtl numbers Pr near 0.8 are presented. The aspect ratio Γ≡D/L of a cylindrical sample was 0.50. For Ra?10(13) the data yielded Nu∝Ra(γ(eff)) with γ(eff)?0.31 and Re(eff)∝Ra(ζ(eff)) with ζ(eff)?0.43, consistent with classical turbulent RBC. After a transition region for 10(13)?Ra?5×10(14), where multistability occurred, we found γ(eff)?0.38 and ζ(eff)=ζ?0.50, in agreement with the results of Grossmann and Lohse for the large-Ra asymptotic state with turbulent boundary layers which was first predicted by Kraichnan.