Azimuthal symmetry, flow dynamics, and heat transport in turbulent thermal convection in a cylinder with an aspect ratio of 0.5

Dynamics and length scales in vertical convection of liquid metals

Using complementary experiments and direct numerical simulations, we study turbulent thermal convection of a liquid metal (Prandtl number $\textit {Pr}\approx 0.03$ ) in a box-shaped container, where two opposite square sidewalls are heated/cooled. The global response characteristics like the Nusselt number ${\textit {Nu}}$ and the Reynolds number $\textit {Re}$ collapse if the side height $L$ is used as the length scale rather than the distance $H$ between heated and cooled vertical plates. These results are obtained for various Rayleigh numbers $5\times 10^3\leq {\textit {Ra}}_H\leq 10^8$ (based on $H$ ) and the aspect ratios $L/H=1, 2, 3$ and $5$ . Furthermore, we present a novel method to extract the wind-based Reynolds number, which works particularly well with the experimental Doppler-velocimetry measurements along vertical lines, regardless of their horizontal positions. The extraction method is based on the two-dimensional autocorrelation of the time–space data of the vertical velocity.

Centrifugal-Force-Induced Flow Bifurcations in Turbulent Thermal Convection

An important and unresolved issue in rotating thermal turbulence is when the flow starts to feel the centrifugal effect. This onset problem is studied here by a novel experiment in which the centrifugal force can be varied over a wide range at fixed Rossby numbers by offsetting the apparatus from the rotation axis. Our experiment clearly shows that the centrifugal force starts to separate the hot and cold fluids at the onset Froude number 0.04. Additionally, this flow bifurcation leads to an unexpected heat transport enhancement and the existence of an optimal state. Based on the dynamical balance and characteristics of local flow structures, both the onset and optimal states are quantitatively explained.

Temperature Fluctuation Profiles in Turbulent Thermal Convection: A Logarithmic Dependence versus a Power-Law Dependence

We report an experimental measurement of the rms temperature (σ_{T}) profiles in two regions inside a large aspect ratio (Γ=4.2) rectangular convection cell. It is found that, in the region where the boundary layer is sheared by a large-scale wind, σ_{T} has a power-law dependence on the vertical distance (z) from the plate, whereas in the region where plumes are abundant, σ_{T} has a logarithmic dependence on z. The power-law profile may be understood by balancing the inertia force and the viscous force in the equations of motion, and the logarithmic profile may be understood in terms of the balance between the buoyancy and the inertia forces. When normalized by a convective temperature scale, θ_{*}, the profiles of σ_{T} collapse onto a single curve for different values of the Rayleigh number. This shows that the convective temperature first proposed by Deardorff is the suitable temperature scale outside the thermal boundary layer for both logarithmic and power-law profiles. Our finding suggests a strong connection between plumes and the logarithmic rms temperature profile. The present Letter reveals that multiple force balance mechanisms can coexist in the bulk of highly turbulent flows.

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.

Effect of aspect ratio on vortex distribution and heat transfer in rotating Rayleigh-Bénard convection

Numerical and experimental data for the heat transfer as a function of the Rossby number Ro in turbulent rotating Rayleigh-Bénard convection are presented for the Prandtl number Pr=4.38 and the Rayleigh number Ra=2.91×10(8) up to Ra=4.52×10(9). The aspect ratio Γ≡D/L, where L is the height and D the diameter of the cylindrical sample, is varied between Γ=0.5 and 2.0. Without rotation, where the aspect ratio influences the global large-scale circulation, we see a small-aspect-ratio dependence in the Nusselt number for Ra=2.91×10(8). However, for stronger rotation, i.e., 1/Ro>>1/Ro(c), the heat transport becomes independent of the aspect ratio. We interpret this finding as follows: In the rotating regime the heat is mainly transported by vertically aligned vortices. Since the vertically aligned vortices are local, the aspect ratio has a negligible effect on the heat transport in the rotating regime. Indeed, a detailed analysis of vortex statistics shows that the fraction of the horizontal area that is covered by vortices is independent of the aspect ratio when 1/Ro>>1/Ro(c). In agreement with the results of Weiss et al. [Phys. Rev. Lett. 105, 224501 (2010)], we find a vortex-depleted area close to the sidewall. Here we show that there is also an area with enhanced vortex concentration next to the vortex-depleted edge region and that the absolute widths of both regions are independent of the aspect ratio.

Connecting flow structures and heat flux in turbulent Rayleigh-Bénard convection

The aspect ratio (Γ) dependence of the heat transfer (Nusselt number Nu in dimensionless form) in turbulent (two-dimensional) Rayleigh-Bénard convection is numerically studied in the regime 0.4≤Γ≤1.25 for Rayleigh numbers 10(7)≤Ra≤Ra(9) and Prandtl numbers Pr=0.7 (gas) and 4.3 (water). Nu(Γ) shows a very rich structure with sudden jumps and sharp transitions. We connect these structures to the way the flow organizes itself in the sample and explain why the aspect ratio dependence of Nu is more pronounced for small Pr. Even for fixed Γ different turbulent states (with different resulting Nu) can exist, between which the flow can or cannot switch. In the latter case the heat transfer thus depends on the initial conditions.

Azimuthal motion, reorientation, cessation, and reversal of the large-scale circulation in turbulent thermal convection: a comparative study in aspect ratio one and one-half geometries

We report a systematic experimental study of the orientation and the flow strength of the large-scale circulation (LSC) in water-filled cylindrical Rayleigh-Bénard convection cells with aspect ratios 2.3, 1, and 0.5 by both direct velocity measurement and the indirect multithermal-probe measurement. Unlike its weak effect in the system's global heat transport, the aspect ratio Gamma is found to play an important role in the dynamics of the azimuthal motion of the LSC. It is found that in larger Gamma geometries the azimuthal motion of the LSC's vertical plane is confined in smaller azimuthal region than that in smaller Gamma geometries. The twisting motion between top and bottom parts of the LSC observed in the Gamma=1 geometry is found to be absent in the Gamma=1/2 case. It is found that in the Gamma=1/2 geometry the orientational change mid R:Deltavarphimid R: through a reorientation has an exponential distribution, in contrast to the power-law distribution for the Gamma=1 case. Despite the difference in orientational change, the occurrence of the reorientations is a Poisson process in both geometries. Using the conditional average of the time interval between adjacent cessations or reversals on the rebound flow strength, we demonstrate the possibility to empirically predict when the next cessation or reversal will most likely occur if the rebound flow strength of the preceding cessation or reversal is given.

Comparative experimental study of local mixing of active and passive scalars in turbulent thermal convection

We investigate experimentally the statistical properties of active and passive scalar fields in turbulent Rayleigh-Bénard convection in water, at Ra approximately 10;{10} . Both the local concentration of fluorescence dye and the local temperature are measured near the sidewall of a rectangular cell. It is found that, although they are advected by the same turbulent flow, the two scalars distribute differently. This difference is twofold, i.e., both the quantities themselves and their small-scale increments have different distributions. Our results show that there is a certain buoyant scale based on time domain, i.e., the Bolgiano time scale t_{B} , above which buoyancy effects are significant. Above t_{B} , temperature is active and is found to be more intermittent than concentration, which is passive. This suggests that the active scalar possesses a higher level of intermittency in turbulent thermal convection. It is further found that the mixing of both scalar fields are isotropic for scales larger than t_{B} even though buoyancy acts on the fluid in the vertical direction. Below t_{B} , temperature is passive and is found to be more anisotropic than concentration. But this higher degree of anisotropy is attributed to the higher diffusivity of temperature over that of concentration. From the simultaneous measurements of temperature and concentration, it is shown that two scalars have similar autocorrelation functions and there is a strong and positive correlation between them.

Modeling the dynamics of a free boundary on turbulent thermal convection

Based on our previous experimental study, we present a one-dimensional phenomenological model of a thermal blanket floating on the upper surface of a thermally convecting fluid. The model captures the most important interactions between the floating solid and the fluid underneath. By the thermal blanketing effect, the presence of the solid plate modifies the flow structure below; in turn, the flow exerts a viscous drag that causes the floating boundary to move. An oscillatory state and a trapped state are found in this model, which is in excellent agreement with experimental observations. The model also offers details on the transition between the states, and gives useful insights on this coupled system without the need for full-scale simulations.

Cessations and reversals of the large-scale circulation in turbulent thermal convection

We present an experimental study of cessations and reversals of the large-scale circulation (LSC) in turbulent thermal convection in a cylindrical cell of aspect ratio (Gamma) 1/2 . It is found that cessations and reversals of the LSC occur in Gamma = 1/2 geometry an order-of-magnitude more frequently than they do in Gamma=1 cells, and that after a cessation the LSC is most likely to restart in the opposite direction, i.e., reversals of the LSC are the most probable cessation events. This contrasts sharply to the finding in Gamma=1 geometry and implies that cessations in the two geometries are governed by different dynamics. It is found that the occurrence of reversals is a Poisson process and that a stronger rebound of the flow strength after a reversal or cessation leads to a longer period of stability of the LSC. Several properties of reversals and cessations in this system are found to be statistically similar to those of geomagnetic reversals. A direct measurement of the velocity field reveals that a cessation corresponds to a momentary decoherence of the LSC.

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.

Azimuthal motion of the mean wind 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 x 10(9) to 1 x 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.

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.