The progress in our understanding of several aspects of turbulent Rayleigh-Benard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the dynamics of the large scale convection roll are addressed as well. The review ends with a list of challenges for future research on the turbulent Rayleigh-Benard system.

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Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection

13. 벼잎선충의 약제처리 방법별 방제 효과

The properties of the structure functions and other small-scale quantities in turbulent Rayleigh-Benard convection are reviewed, from an experimental, theoretical, and numerical point of view. In particular, we address the question of whether, and if so where in the flow, the so-called Bolgiano-Obukhov scaling exists, i.e., Sθ(r) ∼ r2/5 for the second-order temperature structure function and Su(r) ∼ r6/5 for the second-order velocity structure function. Apart from the anisotropy and inhomogeneity of the flow, insufficiently high Rayleigh numbers, and intermittency corrections (which all hinder the identification of such a potential regime), there are also reasons, as a matter of principle, why such a scaling regime may be limited to at most a decade, namely the lack of clear scale separation between the Bolgiano length scale LB and the height of the cell.

Small-Scale Properties of Turbulent Rayleigh-Bénard Convection

Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Benard 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-Benard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.

https://link.springer.com/content/pdf/10.1140%2Fepje%2Fi2012-12058-1.pdf

New perspectives in turbulent Rayleigh-Bénard convection.

Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

We report an experimental study of the three-dimensional spatial structure of the low-frequency temperature oscillations in a cylindrical Rayleigh-Benard convection cell. Through simultaneous multipoint temperature measurements it is found that, contrary to the popular scenario, thermal plumes are emitted neither periodically nor alternately, but randomly and continuously, from the top and bottom plates. We further identify a new flow mode-the sloshing mode of the large-scale circulation (LSC). This sloshing mode, together with the torsional mode of the LSC, are found to be the origin of the oscillation of the temperature field.

Origin of the Temperature Oscillation in Turbulent Thermal Convection

We present an experimental study of the azimuthal motion of the mean wind in turbulent thermal convection. The experiments were conducted with cylindrical convection cells of unity aspect ratio and over the range of the Rayleigh number from $1\ifmmode\times\else\texttimes\fi{}{10}^{9}$ to $1\ifmmode\times\else\texttimes\fi{}{10}^{10}$. The azimuthal angle of the circulation plane of the mean wind was measured using both the particle image velocimetry and flow-visualization techniques. It is found that the azimuthal motion consists of erratic fluctuations and a time-periodic oscillation. The orientation of the wind is found to be ``locked,'' i.e., it fluctuates about a preferred direction most of the time with all other orientations appearing as ``transient states,'' and large excursions of the azimuthal angle often result in a net rotation which takes the wind back to the preferred orientation. The rate of erratic rotation of the circulation plane is found to have a strong dependence on Ra. Our result suggests that the oscillatory motion of the wind in its vertically oriented circulation plane and the orientational oscillation of the circulation plane itself have the same dynamic origin.

Azimuthal motion of the mean wind in turbulent thermal 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.

Morphological evolution of thermal plumes in turbulent Rayleigh-Bénard convection.

We report measurements of the instantaneous viscous boundary layer (BL) thickness delta(v)(t) in turbulent Rayleigh-Benard convection. It is found that delta(v)(t) obtained from the measured instantaneous two-dimensional velocity field exhibits intermittent fluctuations. For small values, delta(v)(t) obeys a lognormal distribution, whereas for large values, the distribution of delta(v)(t) exhibits an exponential tail. The variation of delta(v)(t) with time is found to be driven by the fluctuations of the large-scale mean-flow velocity, and the local horizontal velocities close to the plate can be used as an instant measure of this variation. It is further found that in the present parameter range of the experiment, the mean velocity profile measured in the laboratory frame can be brought into coincidence with the theoretical Prandtl-Blasius laminar BL profile, if it is resampled relative to the time-dependent frame of delta(v)(t).

Measured instantaneous viscous boundary layer in turbulent Rayleigh-Bénard convection.

We investigate the statistical properties of the kinetic and thermal energy dissipation rates in two-dimensional (2-D) turbulent Rayleigh–Benard (RB) convection. Direct numerical simulations were carried out in a box with unit aspect ratio in the Rayleigh number range for Prandtl numbers and 5.3. The probability density functions (PDFs) of both dissipation rates are found to deviate significantly from a log-normal distribution. The PDF tails can be well described by a stretched exponential function, and become broader for higher Rayleigh number and lower Prandtl number, indicating an increasing degree of small-scale intermittency with increasing Reynolds number. Our results show that the ensemble averages and scale as , which is in excellent agreement with the scaling estimated from the two global exact relations for the dissipation rates. By separating the bulk and boundary-layer contributions to the total dissipations, our results further reveal that and are both dominated by the boundary layers, corresponding to regimes and in the Grossmann–Lohse (GL) theory (J. Fluid Mech., vol. 407, 2000, pp. 27–56). To include the effects of thermal plumes, the plume–background partition is also considered and is found to be plume dominated. Moreover, the boundary-layer/plume contributions scale as those predicted by the GL theory, while the deviations from the GL predictions are observed for the bulk/background contributions. The possible reasons for the deviations are discussed.

Quan Zhou

Papers

Origin of the Temperature Oscillation in Turbulent Thermal Convection

Azimuthal motion of the mean wind in turbulent thermal convection.

Morphological evolution of thermal plumes in turbulent Rayleigh-Bénard convection.

Measured instantaneous viscous boundary layer in turbulent Rayleigh-Bénard convection.

Statistics of kinetic and thermal energy dissipation rates in two-dimensional turbulent Rayleigh–Bénard convection