Onset of coherent 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.

Dynamics of large-scale quantities in Rayleigh-Bénard convection

In this paper we estimate the relative strengths of various terms of the Rayleigh-Bénard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity U or the Péclet number that is applicable for arbitrary Rayleigh number Ra and Prandtl number Pr. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling from the theoretical prediction of Ra^{1/2} to the experimentally observed scaling of nearly Ra^{0.3}.

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.

Origin of buckling phenomenon during drying of micrometer-sized colloidal droplets

The origin of the buckling of micrometer-sized colloidal droplets during evaporation-induced self-assembly (EISA) has been elucidated using electron microscopy and small-angle neutron scattering. Doughnut-like assembled grains with varying aspect ratios are formed during EISA at different physicochemical conditions. It has been revealed that this phenomenon is better explained by an existing hypothesis based on the formation of a viscoelastic shell of nanoparticles during drying than by other existing hypotheses based on the inertial instability of the initial droplets and hydrodynamic instability due to thermocapillary forces. This conclusion was further supported by the arrest of buckling through modification of the colloidal interaction in the initial dispersion.

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.

Small-scale turbulent fluctuations beyond Taylor's frozen-flow hypothesis

The space-time cross-correlation function C(T)(r,τ) of local temperature fluctuations in turbulent Rayleigh-Bénard convection is obtained from simultaneous two-point time series measurements. The obtained C(T)(r,τ) is found to have the scaling form C(T)(r(E),0) with r(E)=[(r-Uτ)(2)+V(2)τ(2)](1/2), where U and V are two characteristic velocities associated with the mean and rms velocities of the flow. The experiment verifies the theory and demonstrates its applications to a class of turbulent flows in which the requirement of Taylor's frozen flow hypothesis is not met.

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.

Numerical and experimental investigation of structure-function scaling in turbulent Rayleigh-Bénard convection

Direct numerical simulation and stereoscopic particle image velocimetry of turbulent convection are used to gather spatial data for the calculation of structure functions. We wish to add to the ongoing discussion in the literature whether temperature acts as an active or passive scalar in turbulent convection, with consequences for structure-function scaling. The simulation results show direct confirmation of the scalings derived by Bolgiano and Obukhov for turbulence with an active scalar for both velocity and temperature statistics. The active-scalar range shifts to larger scales when the forcing parameter (Rayleigh number) is increased. Furthermore, a close inspection of local turbulent length scales (Kolmogorov and Bolgiano lengths) confirms conjectures from earlier studies that the oft-used global averages are not suited for the interpretation of structure functions. In the experiment, a characterization of the domain-filling large-scale circulation of confined convection is carried out for comparison with other studies. The measured velocity fields are also used to calculate velocity structure functions, further confirming the Bolgiano-Obukhov scalings when interpreted with the local turbulent length scales found in the simulations. An extended self-similarity analysis shows that the relative scalings are different for the Kolmogorov and Bolgiano-Obukhov regimes.

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.

Structure of the thermal boundary layer for turbulent Rayleigh-Bénard convection of air in a long rectangular enclosure

Measurements of the temperature distribution were performed in the upper (cold) boundary layer of a rectangular Rayleigh-Bénard cell with aspect ratios Gamma(x) = 5 and Gamma(y) = 1 using air with Prandtl number Pr = 0.71 as the working fluid. The range of investigated Rayleigh numbers was from Ra approximately 6 x 10(7) to Ra approximately 6 x 10(8), and the measurements were taken at two different positions with the purpose of understanding the variation of the properties of the thermal boundary layer along the cell. We present profiles of the mean temperature, rms temperature fluctuations, skewness, and kurtosis as a function of the distance from the cooling plate from which we extract scaling exponents and boundary layer thicknesses. Whereas most of these quantities are found to depend monotonically on the Rayleigh number for the peripheral measurement position, their values at the central measurement position exhibit a high degree of variability. These observations indicate that the properties of the thermal boundary layer in large-aspect-ratio convection can have strong spatial variations.

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.

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.

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.

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.

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.

Dynamics of air avalanches in the access pit of an underground quarry

Temperature measurements have been performed in the vertical access pit of an underground quarry. During autumn, air avalanches induce an initial thermal feedback and a stationary mixing state characterized by spatially coherent broad-band fluctuations with a standard deviation of about 0.2 degrees C, linearly increasing with the inside-minus-outside temperature difference. Phase changes of water are shown to contribute to the onset condition, the feedback, and the stationary mixing state. This experiment may give insight on turbulent thermal and compositional convection with nonadiabatic boundaries.

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 and Rayleigh number dependence of the Reynolds number in turbulent thermal convection

The Prandtl and Rayleigh number dependences of the Reynolds number in turbulent thermal convection following from the unifying theory by Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000); Phys. Rev. Lett. 86, 3316 (2001)] are presented and compared with various recent experimental findings. This dependence Re(Ra,Pr) is more complicated than a simple global power law. For Pr=5.5 and 10(8)<Ra<10(10) the effective or local power law exponent of Re as a function of Ra is definitely less than 0.50, namely, Re approximately Ra(0.45), in agreement with Qiu and Tong's experimental findings [Phys. Rev. E 64, 036304 (2001)]. We also calculated the kinetic boundary layer width. Both in magnitude and in Ra scaling it is consistent with the data.