Temperature oscillations in turbulent Rayleigh-Bénard convection

Symmetry-breaking-induced rare fluctuations in a time-delay dynamic system

Inspired by the experimental and numerical findings, we study the dynamic instabilities of two coupled nonlinear delay differential equations that are used to describe the coherent oscillations between the top and bottom boundary layers in turbulent Rayleigh-Bénard convection. By introducing two sensitivity parameters for the instabilities of the top and bottom boundary layers, we find three different types of solutions, namely in-phase single-period oscillations, multi-period oscillations and chaos. The chaos solution contains rare but large amplitude fluctuations. The statistical properties of these fluctuations are consistent with those observed in the experiment for the massive eruption of thermal plumes, which causes random reversals of the large-scale circulation in turbulent Rayleigh-Bénard convection. Our study thus provides new insights into the origin of rare massive eruptions and sudden changes of large-scale flow pattern that are often observed in convection systems of geophysical and astrophysical scales.

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.

Enhanced and reduced heat transport in turbulent thermal convection with polymer additives

We present an experimental study of turbulent Rayleigh-Bénard convection with polymer additives made in two convection cells, one with a smooth top and bottom plates and the other with a rough top and bottom plates. For the cell with smooth plates, a reduction of the measured Nusselt number (Nu) was observed. Furthermore, the amount of Nu reduction increases with increasing polymer concentration (c), reaching ~12% for c = 120 ppm and an apparent leveling off thereafter. For the cell with rough plates, however, an enhancement (~4%) of Nu was observed when the polymer concentration is greater than 120 ppm. This increase in Nu is corroborated by an increased large-scale circulation (LSC) velocity in the same cell when polymers are added. In contrast, the LSC velocity in the smooth cell is found to be essentially the same with and without polymers. It is further found that in the smooth cell the rms values of the global Nu, σ(Nu), and that of the local temperature, σ(T), both exhibit similar dependence on c as Nu itself. In contrast, σ(Nu) and σ(T) in the rough cell are found to be essentially independent of c.

Coherent oscillations of turbulent Rayleigh-Bénard convection in a thin vertical disk

A well-defined oscillation is observed in the power spectrum of several fluctuating signals in turbulent Rayleigh-Bénard convection occurring in a thin vertical disk filled with water. The experiment reveals that the coherent oscillations are produced by periodic emission of thermal plumes, which gives rise to periodic pulses of forcing, resulting in a pulsed large-scale circulation in the thin cell. The experimental results agree well with the theoretical predictions made from two coupled nonlinear delayed equations.

Spontaneous flow reversals in Rayleigh-Bénard convection of a liquid metal

We report a finding of spontaneous flow reversals of roll-like patterns in liquid gallium Rayleigh-Bénard convection. The vessel has a square geometry with an aspect ratio of 5, and a horizontal magnetic field is applied to align the rolls. The flow patterns were visualized by ultrasonic velocity measurements, and the processes of the reversal were clearly observed. The basic flow pattern observed in the vessel is a four-roll structure with its axis parallel to the magnetic field. Emergence of a new circulation at a corner of the vessel causes flow reversal with reorganization of the whole pattern. The flow keeps relatively steady four-roll structure for most of the duration, while the reversal of it is over in a short time. The reversals of the flow occur randomly with the interval time between reversals being much longer than the circulation time.

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.

Origin of the temperature oscillation in turbulent thermal convection

We report an experimental study of the three-dimensional spatial structure of the low-frequency temperature oscillations in a cylindrical Rayleigh-Bénard 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.

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.

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.

Measured oscillations of the velocity and temperature fields in turbulent Rayleigh-Bénard convection in a rectangular cell

Temperature and velocity oscillations have been found in a rectangular Rayleigh-Bénard convection cell, in which one large-scale convection roll exists. At Rayleigh number Ra=8.9x10(11) and Prandtl number Pr=4, temperature oscillations can be observed in most parts of the system and the oscillation period remains almost constant, tT=74+/-2 s. Velocity oscillation can only be found in its horizontal component vy (perpendicular to the large-scale circulation plane) near the cell sidewall, its oscillation period is also constant, tv=65+/-2 s, at these positions. Temperature and velocity oscillations have different Ra dependences, which are, respectively, indicated by the Péclect number PeT=0.55Ra0.47 and Pev=0.28Ra0.50. In comparison to the case of a cylindrical cell, we find that velocity oscillations are affected by the system geometry.

Breakdown of wind in turbulent thermal convection

We report experiments on turbulent Rayleigh-Bénard convection of air in a cylindrical large-scale facility with a diameter of 7 meters and Rayleigh numbers up to Ra approximately 10(12). The facility is used to explore the structure of the large-scale circulation for continuously varying aspect ratios between Gamma approximately 1 and Gamma approximately 10. Using autocorrelation functions derived from high-resolution time series of temperature and velocity near the cooling plate we demonstrate that the well-known single-roll structure (often called "wind") breaks down when the aspect ratio increases beyond the critical value Gamma(1) = 1.68+/-0.22. We further show that at Gamma(2) = 3.66+/-0.46 a second transition from an oscillatory two-roll structure to an unstable multi-roll structure takes place. The value of Gamma(2) represents a lower bound for the aspect ratio that is necessary to reach homogeneous convection--a turbulent state that is free from the influence of lateral walls.

Long-term persistence of the spatial organization of temperature fluctuation lifetime in turbulent air avalanches

It has been recently proposed that some natural phenomena, such as sunspot occurrence, can be represented by a modulated Markov jitter, which is a high-frequency Markov signal multiplied by a long-term component. The two parameters of this model can be estimated using a nonlinear method based on absolute derivatives. This analysis is applied here to a different physical system: the temperature time series measured during air avalanches in the vertical access pit of an underground quarry. The thermal fluctuations associated with these turbulent flows, driven by the external temperature forcing, actually appear as another practical realization of a modulated Markov jitter. One parameter of the model provides the lifetime of the temperature fluctuations, which can be estimated as a function of time and position. The obtained lifetime is of the order of 10 to 25 min , and is remarkably constant in time for each sensor, independently of the amplitude of the forcing. Furthermore, a significant and persistent spatial structure is observed, revealing a long-term intrinsic organization of the turbulent air flows in the pit. Such a stable spatial organization may reflect a general feature of turbulent phenomena.

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.

Scaling of the Reynolds number in turbulent thermal convection

A riddle in turbulent thermal convection is the apparent dispersion from 0.42 to 0.5 in the value of the scaling exponent of experimentally measured Reynolds number Re approximately Ragamma, where Ra is the Rayleigh number. The measured Re may be divided into two groups: one based on the circulation frequency of the mean wind and the other based on a directly measured velocity. With new experimental results we show that in frequency measurements the dispersion in gamma is a result of the evolution in the circulation path of the wind, and that in the velocity measurements it is caused by the inclusion of a counterflow in the mean velocity. When these factors are properly accounted for both groups give gamma=0.5, which may imply that a single mechanism is driving the flow for both low and high values of Ra.

Three-dimensional flow structures and dynamics of turbulent thermal convection in a cylindrical cell

The technique of particle image velocimetry is used to study the velocity field of turbulent Rayleigh-Bénard convection in an aspect-ratio-1 cylindrical cell filled with water. By measuring the two-dimensional (2D) velocity vector map in different vertical cross sections of the cell, we investigate the 3D structures and dynamics of turbulent thermal convection. The experiment reveals how thermal plumes synchronize their emissions and organize their motions spatially between the top and bottom plates, leading to an oscillatory motion in the bulk region of the fluid with a period equal to twice the plume's cell-crossing time. From the measured instantaneous velocity vector map, we find the phase relationship between the velocity components along different directions and at different positions in a 2D plane. These phase relations illustrate how the convecting fluid in different regions of the cell interact with each other and generate a synchronized and coherent motion in a closed system.

Extraction of plumes in turbulent thermal convection

We present a scheme to extract the velocity of buoyant structures in turbulent thermal convection from simultaneous local velocity and temperature measurements. Applying this scheme to measurements taken at positions within the convection cell where the buoyant structures are dominated by plumes, we obtain the temperature dependence of the plume velocity and understand our results using the equations of motion. We further obtain the scaling behavior of the average local heat flux in the vertical direction at the cell center with the Rayleigh number and find that the scaling exponent is different from that measured for the Nusselt number. This difference leads to the conclusion that heat cannot be mainly transported through the central region of the convection cell.

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

A systematic study of the local convective heat transport in turbulent thermal convection is carried out in small-aspect-ratio cells filled with water. The local convective heat flux is obtained from the simultaneous velocity and temperature measurements over varying Rayleigh numbers and spatial positions across the entire convection cell. Large fluctuations of the local convective heat flux are found mainly in the vertical direction and they are determined primarily by the thermal plumes in the system. The experiment reveals the spatial distribution of the local convective heat flux in a closed cell and thus settles a long-debated issue on how heat is transported in small-aspect-ratio cells.

Clustering of plumes in turbulent convection

Turbulent Rayleigh-Bénard convection produces fields of intense updrafts and downdrafts that are responsible for much of the vertical heat transport. These structures, called plumes or thermals, have horizontal scales comparable to the thicknesses of the boundary layers in which they arise. In the three-dimensional numerical simulations reported here, we have observed that convective plumes organize themselves into clusters with horizontal scales that grow with time and reach the width of the computational domain. In this two-scale process, kinetic energy is transferred mainly to low horizontal wave numbers while the sizes of individual plumes remain on the scale of the boundary layer thickness.

Plume motion and large-scale circulation in a cylindrical Rayleigh-Bénard cell

We used the time correlation of shadowgraph images to determine the angle Theta of the horizontal component of the plume velocity above (below) the center of the bottom (top) plate of a cylindrical Rayleigh-Bénard cell of aspect ratio Gamma identical with D/L=1 (D is the diameter and L approximately 87 mm is the height) in the Rayleigh-number range 7 x 10(7)</=R</=3 x 10(9) for a Prandtl number sigma=6. We expect that Theta gives the direction of the large-scale circulation. It oscillates time periodically. Near the top and bottom plates Theta(t) has the same frequency but is anticorrelated.

Conductive and dielectric defects, and anisotropic and isotropic turbulence in liquid crystals: Electric power fluctuation measurements

Fluctuations of the injected electric power during electroconvection (EHC) of liquid crystals are reported in both the conductive and the dielectric regime of convection. The amplitude and the frequency of the fluctuations, as well as the probability density functions have been compared in these two regimes and substantial differences have been found both in defect turbulence of EHC and at the DSM1-->DSM2 transition.

Particle image velocimetry measurement of the velocity field in turbulent thermal convection

The spatial structure of the velocity field in turbulent Rayleigh-Bénard convection in water has been measured using the particle image velocimetry technique, with the Rayleigh number Ra varying from 9 x 10(8) to 9 x 10(11) and the Prandtl number remaining approximately constant (Pr approximately 4). The study provides a direct confirmation that a rotatory mean wind indeed persists for the highest value of Ra reached in the experiment. The measurement reveals that the mean flow in the central region of the convection cell is of the shape of a coherent elliptical rotating core for Ra below 1 x 10(10). Above this Ra, the orientation of the elliptical core changes by a 90 degrees angle and an inner core rotating at a lower rate inside the original bulk core emerges. It is further found that the rotation frequencies of the inner core and the outer shell have distinct scalings with Ra; the scaling exponent for the outer-shell is 0.5 and it is 0.4 for the inner core. From the measured rms and skewness distributions of the velocity field, we find that velocity fluctuations at the cell center are neither homogeneous nor isotropic. The turbulent energy production fields further reveal that the mean wind is not driven by turbulent fluctuations associated with Reynolds stress.

Persistent global power fluctuations near a dynamic transition in electroconvection

This is a study of the global fluctuations in power injection and light transmission through a liquid crystal just above the onset of electroconvection. The source of the fluctuations is identified as the creation and annihilation of defects. They are spatially uncorrelated and yet temporally correlated. The temporal correlation is seen to persist for extremely long times. There seems to be an especially close relation between defect creation or annihilation in electroconvection and thermal plumes in Rayleigh-Bénard convection.

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.