Large-scale coherent rotation and oscillation in turbulent thermal 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.

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.

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.

Wind and boundary layers in Rayleigh-Bénard convection. I. Analysis and modeling

The aim of this paper is to contribute to the understanding of and to model the processes controlling the amplitude of the wind of Rayleigh-Bénard convection. We analyze results from direct simulation of an L/H=4 aspect-ratio domain with periodic sidewalls at Ra=(10(5), 10(6), 10(7), 10(8)) and at Pr=1 by decomposing independent realizations into wind and fluctuations. It is shown that, deep inside the thermal boundary layer, horizontal heat fluxes exceed the average vertical heat flux by a factor of 3 due to the interaction between the wind and the mean temperature field. These large horizontal heat fluxes are responsible for spatial temperature differences that drive the wind by creating pressure gradients. The wall fluxes and turbulent mixing in the bulk provide damping. Using the direct numerical simulation results to parametrize the unclosed terms, a simple model capturing the essential processes governing the wind structure is derived. The model consists of two coupled differential equations for wind velocity and temperature amplitude. The equations indicate that the formation of a wind structure is inevitable due to the positive feedback resulting from the interaction between the wind and temperature field. Furthermore, the wind velocity is largely determined by the turbulence in the bulk rather than by the wall-shear stress. The model reproduces the Ra dependence of wind Reynolds number and temperature amplitude.

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.

Oscillating large-scale circulation in turbulent Rayleigh-Bénard convection

We report on the dynamics and structure of the turbulent velocity field in a high-Rayleigh-number (Ra = 5.9 x 10(8))thermal convection cell with an aspect ratio of 4. Spectral density functions (measured with laser Doppler velocimetry) indicated the existence of a large-scale periodic component. The long-time mean flow field (measured with particle image velocimetry) revealed that the large-scale circulation in the aspect-ratio-4 cell consists of two corotating rolls. The periodicity in the flow could be traced back to the alternating growth and decay of these rolls.

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.

Critical fluctuation of wind reversals in convective turbulence

The irregular reversals of wind direction in convective turbulence are found to have fluctuating intervals that can be related, under certain circumstances, to critical behavior. In particular, by focusing on its temporal evolution, the net magnetization of a two-dimensional Ising lattice of finite size is observed to fluctuate in the same way. Detrended fluctuation analysis of the wind reversal time series results in a scaling behavior that agrees remarkably well with that of the Ising problem. The specific properties found here, as well as the lack of an external tuning parameter, also suggest that the wind reversal phenomenon exhibits signs of self-organized criticality.

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.

Mean wind in convective turbulence of mercury

The large-scale circulation, often called "wind," in the confined thermal turbulence of mercury is studied experimentally. The instantaneous velocity profile at 128 points is directly measured using ultrasonic velocimetry. The periodic velocity oscillation is observed in the case of the aspect-ratio Gamma = 1,2 but not in Gamma = 0.5. Its peak frequency is scaled by f(c) proportional Ra(gamma(c)), where Ra is the Rayleigh number and gamma(c) = 0.43,0.45 for Gamma = 1,2. f(c) is close to the wind circulation frequency f(p), and has the same order of transit time from the bottom to the top of the convection cell. A single roll circulation is expected in Gamma = 1; however, axisymmetric toroidal rings may exist near the upper and lower plate for Gamma = 0.5, which are stable up to Ra = 7 x 10 (10).

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.

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.

Intermittency of velocity fluctuations in turbulent thermal convection

We analyze velocity fluctuations in turbulent Rayleigh-Bénard convection. The velocity measurements were taken at the center of an aspect-ratio-one convection cell filled with water. The measured probability density functions of the velocity difference over a time interval tau are found to change with tau, indicating that the velocity fluctuations are intermittent. The velocity intermittency can be well characterized by the She-Leveque hierarchical structure. Our analyses further show that the vertical velocity component has distinct statistical features from the horizontal components. This result indicates that the vertical direction is special and buoyancy is important even at the center of the convection cell.

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.

Response maxima in modulated turbulence

Isotropic and homogeneous turbulence driven by an energy input modulated in time is studied within a variable range mean-field theory. The response of the system, observed in the second-order moment of the large-scale velocity difference D(L,t)=<<(u(x+L)-u(x))(2)>> proportional, variant Re(2)(t), is calculated for varying modulation frequencies omega and weak modulation amplitudes. For low frequencies the system follows the modulation of the driving with almost constant amplitude, whereas for higher driving frequencies the amplitude of the response decreases on average proportional, variant 1/omega. In addition, at certain frequencies the amplitude of the response either almost vanishes or is strongly enhanced. These frequencies are connected with the frequency scale of the energy cascade and multiples thereof.

Temperature oscillations in turbulent Rayleigh-Bénard convection

A systematic study of temperature oscillations in turbulent thermal convection was carried out in two aspect-ratio-one convection cells filled with water. Temperature correlation functions and local velocity fluctuations were measured over varying Rayleigh numbers and spatial positions across the entire cell. These measurements fully characterize the spatial structure of the temperature oscillation and reveal the mixing and emission dynamics of the thermal plumes near the conducting surface. 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 5 x 10(7). Above Ra(c) the measured temperature correlation functions show a well-defined oscillation with a finite coherence time. The oscillation period is found to be twice as large as the cell crossing time. The experiment demonstrates how the thermal plumes in a closed cell organize themselves both in space and time and generate coherent oscillations in a turbulent environment.

Prandtl number dependence of the viscous boundary layer and the Reynolds numbers in Rayleigh-Bénard convection

We report results from high Prandtl number turbulent thermal convection experiments. The viscous boundary layer and the Reynolds number are measured in four different fluids over wide ranges of the Prandtl number Pr and the Rayleigh number Ra, all in a single convection cell of unity aspect ratio. We find that the normalized viscous layer thickness may be represented as delta(v)/L=0.65Pr(0.24)Ra(-0.16). The Reynolds number based on the oscillation frequency of the large-scale flow is found as Re(o)(Ra,Pr)=1.1Ra(0.43)Pr(-0.76) and that based on the rms velocity Re(rms)(Ra,Pr)=0.84Ra(0.40)Pr-0.86. Both the Ra and the Pr exponents of Re(V(m))(Ra,Pr) based on the maximum velocity of the circulating wind appear to vary across the range of Pr covered, changing from 0.5 to 0.68 and -0.88 to -0.95, respectively, as Pr is increased from 6 to 1027.

Mean wind and its reversal in thermal convection

Properties of the mean wind in thermal convection, especially the abrupt reversal of its direction at high Rayleigh numbers, are studied. Measurements made in a closed cylindrical container of aspect ratio 1 are analyzed, and both the long-term and short-term behaviors of the direction reversals are discussed. A first look at the data suggests a Brownian-type process in action, but a closer look suggests the existence of hierarchical features with time scales extending roughly over a decade and a half. A physical model consistent with experimental observations is presented, and the origin of the cutoff scales is discussed. It appears that the generation of the wind as well as the reversal of its direction can be understood in terms of the imbalance between buoyancy effects and friction.

Scaling of the velocity power spectra in turbulent thermal convection

We report measurements of the local velocity in a convection cell filled with water. In the buoyancy subrange (the scales between the Bolgiano scale f(B) and the integral scale f(o)), two scaling regions of the velocity frequency power spectra, separated by the peak frequency f(p) of the dissipation spectra, are found. For f(p)<f<f(B), we observe a power law with the Bolgiano-Obukhov scaling exponent -11/5. For f(o)<f<f(p), an unexpected scaling with an exponent -1.35 is observed. We also found that the velocity power spectra are universal functions with respect to the characteristic scales f(p). and f(B).

Large-scale velocity structures in turbulent thermal convection

A systematic study of large-scale velocity structures in turbulent thermal convection is carried out in three different aspect-ratio cells filled with water. Laser Doppler velocimetry is used to measure the velocity profiles and statistics over varying Rayleigh numbers Ra and at various spatial positions across the whole convection cell. Large velocity fluctuations are found both in the central region and near the cell boundary. Despite the large velocity fluctuations, the flow field still maintains a large-scale quasi-two-dimensional structure, which rotates in a coherent manner. This coherent single-roll structure scales with Ra and can be divided into three regions in the rotation plane: (1) a thin viscous boundary layer, (2) a fully mixed central core region with a constant mean velocity gradient, and (3) an intermediate plume-dominated buffer region. The experiment reveals a unique driving mechanism for the large-scale coherent rotation in turbulent convection.

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.

Scaling properties of the temperature field in convective turbulence

We report the scaling properties of temperature in turbulent convection in water. In the central region of the convection cell, we find that the peak frequency of the temperature dissipation spectra may be identified as the "Bolgiano frequency," with respect to which the temperature power spectra are universal functions; and that the usual inertial range is taken up entirely by the buoyancy subrange, so that a "high frequency" scaling subrange emerges only through an extended-self-similarity-type analysis. Moreover, the buoyancy subrange assumes the value of 2/5 predicted for the Bolgiano-Obukhov scaling only in the central region of the cell; in the mixing zone the exponent for the high frequency scaling exponent has a value of 2/3.

Temperature fluctuations in a convection cell with rough upper and lower surfaces

A turbulent convection experiment is conducted in a cell with rough upper and lower surfaces. Temperature statistics, frequency power spectrum, and thermal dissipation are measured over varying Rayleigh numbers in the central region of the cell. The temperature histogram in the rough cell is found to have the same exponential shape as that in the smooth cell, but the width of the distribution is increased by approximately 25%. The measured power spectrum shows that temperature fluctuations in the rough cell are increased uniformly across the whole frequency range. The cutoff frequency f(c) of the power spectrum and the time averaged square temperature time derivative <( partial differentialT/ partial differentialt)(2)> are used to characterize the thermal dissipation in turbulent convection. It is found that the normalized f(c) as well as <( partial differentialT/ partial differentialt)(2)> in the smooth and rough cells with different aspect ratios can all be superposed onto a single curve, indicating that the thermal dissipation in these cells is determined by the same mechanism. The experiment suggests that the enhanced heat transport observed in the rough cell is determined primarily by the local dynamics near the upper and lower boundaries.

Spatially correlated temperature fluctuations in turbulent convection

By measuring the degree of spatial correlation in temperature fluctuations at two points separated by a distance perpendicular to the mean flow, we are able to determine the viscous boundary layer thickness in turbulent convection. We demonstrate this method using water as the working fluid and find excellent agreement with directly measured results. Furthermore, from the most probable delay time for a thermal disturbance to successively pass the two temperature probes, we deduce the width of the mixing zone and again find very good agreement between the value obtained and that predicted by theory.