Extraction of plumes in turbulent thermal convection

Robustness of heat transfer in confined inclined convection at high Prandtl number

We investigate the dependency of the magnitude of heat transfer in a convection cell as a function of its inclination by means of experiments and simulations. The study is performed with a working fluid of large Prandtl number, Pr≃480, and at Rayleigh numbers Ra≃10^{8} and Ra≃5×10^{8} in a quasi-two-dimensional rectangular cell with unit aspect ratio. By changing the inclination angle (β) of the convection cell, the character of the flow can be changed from moderately turbulent, for β=0^{∘}, to laminar and steady at β=90^{∘}. The global heat transfer is found to be insensitive to the drastic reduction of turbulent intensity, with maximal relative variations of the order of 20% at Ra≃10^{8} and 10% at Ra≃5×10^{8}, while the Reynolds number, based on the global root-mean-square velocity, is strongly affected with a decay of more than 85% occurring in the laminar regime. We show that the intensity of the heat flux in the turbulent regime can be only weakly enhanced by establishing a large-scale circulation flow by means of small inclinations. However, in the laminar regime the heat is transported solely by a slow large-scale circulation flow which exhibits large correlations between the velocity and temperature fields. For inclination angles close to the transition regime in-between the turbulentlike and laminar state, a quasiperiodic heat-flow bursting phenomenon is observed.

Condensation of Coherent Structures in Turbulent Flows

Coherent structures are ubiquitous in turbulent flows and play a key role in transport. The most important coherent structures in thermal turbulence are plumes. Despite being the primary heat carriers, the potential of manipulating thermal plumes to transport more heat has been overlooked so far. Unlike some other forms of energy transport, such as electromagnetic or sound waves, heat flow in fluids is generally difficult to manipulate, as it is associated with the random motion of molecules and atoms. Here we report how a simple geometrical confinement can lead to the condensation of elementary plumes. The result is the formation of highly coherent system-sized plumes and the emergence of a new regime of convective thermal turbulence characterized by universal temperature profiles and significantly enhanced heat transfer. It is also found that the universality of the temperature profiles and heat transport originate from the geometrical properties of the coherent structures, i.e., the thermal plumes. Therefore, in contrast to the classical regime, boundary layers in this plume-controlled regime are being controlled, rather than controlling.

Flow patterns in inclined-layer turbulent convection

We study the flow patterns of turbulent convection in an inclined layer with a large aspect ratio Γ and moderately high Rayleigh numbers ranging from 9 × 10(4) to 2 × 10(7) based on three-dimensional numerical simulations. The Prandtl number is fixed at σ = 0.7 and the angles of inclination are varied between 5° ≤ θ ≤ 60°. The initial quiescent fluid layer is observed to firstly evolve into a quasi-periodical flow pattern before the turbulent convection is fully developed. The transient flow at earlier times, though elongated along the slope and anisotropic in the directions parallel to the top and bottom plates, becomes isotropic in the final statistically steady state, provided that the Rayleigh number is high (R ≃ 2 × 10(7)) and the angle of inclination is small (θ ≤ 17°). The effect of inclination on the large-scale flow is different from that on individual plumes, which exhibits isotropy and is independent of the angles of inclination for Rayleigh numbers above 5 × 10(6). The regions near the upper and lower sidewalls of the enclosure, considered as extensions of the thermal boundary layer, shrink with increasing Rayleigh numbers and the scaling exponent is about 2/7.

Spatial distribution of heat flux and fluctuations in turbulent Rayleigh-Bénard convection

We numerically investigate the radial dependence of the velocity and temperature fluctuations and of the time-averaged heat flux j ¯(r) in a cylindrical Rayleigh-Bénard cell with aspect ratio Γ=1 for Rayleigh numbers Ra between 2×10^{6} and 2×10^{9} at a fixed Prandtl number Pr=5.2. The numerical results reveal that the heat flux close to the sidewall is larger than in the center and that, just as the global heat transport, it has an effective power law dependence on the Rayleigh number, j ¯(r)∝Ra{γ{j}(r)}. The scaling exponent γ{j}(r) decreases monotonically from 0.43 near the axis (r≈0) to 0.29 close to the sidewalls (r≈D/2). The effective exponents near the axis and the sidewall agree well with the measurements of Shang et al. [Phys. Rev. Lett. 100, 244503 (2008)] and the predictions of Grossmann and Lohse [Phys. Fluids 16, 1070 (2004)]. Extrapolating our results to large Rayleigh number would imply a crossover at Ra≈10^{15}, where the heat flux near the axis would begin to dominate. In addition, we find that the local heat flux is more than twice as high at the location where warm or cold plumes go up or down than in plume depleted regions.

Conditional statistics of thermal dissipation rate in turbulent Rayleigh-Bénard convection

The statistical properties of the thermal dissipation rate in turbulent Rayleigh-Bénard convection in a cylindrical cell are studied by means of three-dimensional direct numerical simulations for a fixed Prandtl number Pr = 0.7 and aspect ratio Γ = 1. The Rayleigh numbers Ra are between 10(7) and 3 × 10(10). We apply a criterion that decomposes the cell volume into two disjoint subsets: the plume-dominated part and the turbulent background part. The plume-dominated set extends over the whole cell volume and is not confined to the boundary layers. It forms a complex spatial skeleton on which the heat is transported in the convection cell and its volume fraction decreases with increasing Rayleigh number. The latter finding holds also when the threshold, which separates both subvolumes, is varied. The Rayleigh number dependence of the mean moments and probability density functions of the thermal dissipation are analyzed on the subvolumes and related to other possible divisions of the convection volume, such as into boundary layer and bulk. The largest thermal dissipation events are always found in the plume-dominated subset.

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.

Structure of viscous boundary layers in turbulent Rayleigh-Bénard convection

Highly resolved profiles of the mean velocity in turbulent Rayleigh-Bénard convection in air are presented and discussed. The present work extends our recently performed experiments at constant aspect ratio [Phys. Rev. Lett. 99, 234504 (2007)] to variable aspect ratios. The experiments cover a range of Rayleigh numbers 10(9)<Ra<10(12) and aspect ratios 1.13<Gamma<11.3 whereas the Prandtl number is fixed at Pr=0.7. The major finding of the present work is that the profiles of the mean horizontal velocity and its fluctuations are virtually invariant against the variation in Ra or Gamma if the wall distance is scaled by the displacement thickness of the boundary layer. Furthermore we have studied typical length scales of the boundary layer and their scaling with Ra and Gamma. Regarding a potential transition of the heat transport toward the ultimate regime we found that the boundary layer Reynolds number remains below Redelta=250 which is significantly lower than the predicted limit.

Measurements of the thermal dissipation field in turbulent Rayleigh-Bénard convection

A systematic study of the thermal dissipation field and its statistical properties is carried out in turbulent Rayleigh-Bénard convection. A local temperature gradient probe consisting of four identical thermistors is made to measure the normalized thermal dissipation rate epsilonN(r) in two convection cells filled with water. The measurements are conducted over varying Rayleigh numbers Ra (8.9x10(8)<approximately Ra<approximately 9.3x10(9)) and spatial positions r across the entire cell. 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 Ra. The other contribution comes from the mean temperature gradient, being concentrated in the thermal boundary layers, and increases with Ra. The experiment provides a complete physical picture about the thermal dissipation field and its statistical properties in turbulent convection.

Lagrangian temperature, velocity, and local heat flux measurement in Rayleigh-Bénard convection

We have developed a small, neutrally buoyant, wireless temperature sensor. Using a camera for optical tracking, we obtain simultaneous measurements of position and temperature of the sensor as it is carried along by the flow in Rayleigh-Bénard convection, at Ra approximately 10;{10}. We report on statistics of temperature, velocity, and heat transport in turbulent thermal convection. The motion of the sensor particle exhibits dynamics close to that of Lagrangian tracers in hydrodynamic turbulence. We also quantify heat transport in plumes, revealing self-similarity and extreme variations from plume to plume.

Scaling laws in the central region of confined turbulent thermal convection

In confined turbulent thermal convection, the velocity is separated into two parts: one that is correlated with some function of the temperature fluctuations, and thus associated with the plume velocity, and the other part, the background velocity, which is uncorrelated with any function of the temperature fluctuations. As a result, one should focus on the plume velocity, and not the whole velocity, and the temperature when studying the scaling behavior. In this paper, a phenomenological theory for the scaling behavior in the central region of confined turbulent thermal convection is presented. The spatial (temporal) plume velocity structure functions are found to have the same scaling behavior as the spatial (temporal) temperature structure functions. For tau> or = taub, where the buoyant scale taub is determined in terms of measurable quantities, the scaling exponents of the temporal temperature structure functions and hence those of the temporal plume velocity structure functions are obtained. These results are checked against experimental measurements, and good agreement is found.

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.