Circulation in Quasi-2D Turbulence: Experimental Observation of the Area Rule and Bifractality.

We present an experimental study of the velocity circulation in a quasi-two-dimensional turbulent flow. We show that the area rule of circulation around simple loops holds in both the forward cascade enstrophy inertial range (ΩIR) and the inverse cascade energy inertial range (EIR): When the side lengths of a loop are all within the same inertial range, the circulation statistics depend on the loop area alone. It is also found that, for circulation around figure-eight loops, the area rule still holds in EIR but is not applicable in ΩIR. In ΩIR, the circulation is nonintermittent; whereas in EIR, the circulation is bifractal: space filling for moments of the order of 3 and below and a monofractal with a dimension of 1.42 for higher orders. Our results demonstrate, as in a numerical study of 3D turbulence [K. P. Iyer et al., Circulation in High Reynolds Number Isotropic Turbulence is a Bifractal, Phys. Rev. X 9, 041006 (2019).PRXHAE2160-330810.1103/PhysRevX.9.041006], that, in terms of circulation, turbulent flows exhibit a simpler behavior than velocity increments, as the latter are multifractals.

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.

Flow Topology Transition via Global Bifurcation in Thermally Driven Turbulence.

We report an experimental observation of a flow topology transition via global bifurcation in a turbulent Rayleigh-Bénard convection. This transition corresponds to a spontaneous symmetry breaking with the flow becomes more turbulent. Simultaneous measurements of the large-scale flow (LSF) structure and the heat transport show that the LSF bifurcates from a high heat transport efficiency quadrupole state to a less symmetric dipole state with a lower heat transport efficiency. In the transition zone, the system switches spontaneously and stochastically between the two long-lived metastable states.

Confined Rayleigh-Bénard, Rotating Rayleigh-Bénard, and Double Diffusive Convection: A Unifying View on Turbulent Transport Enhancement through Coherent Structure Manipulation.

Many natural and engineering systems are simultaneously subjected to a driving force and a stabilizing force. The interplay between the two forces, especially for highly nonlinear systems such as fluid flow, often results in surprising features. Here we reveal such features in three different types of Rayleigh-Bénard (RB) convection, i.e., buoyancy-driven flow with the fluid density being affected by a scalar field. In the three cases different stabilizing forces are considered, namely (i) horizontal confinement, (ii) rotation around a vertical axis, and (iii) a second stabilizing scalar field. Despite the very different nature of the stabilizing forces and the corresponding equations of motion, at moderate strength we counterintuitively but consistently observe an enhancement in the flux, even though the flow motion is weaker than the original RB flow. The flux enhancement occurs in an intermediate regime in which the stabilizing force is strong enough to alter the flow structures in the bulk to a more organized morphology, yet not too strong to severely suppress the flow motions. Near the optimal transport enhancements all three systems exhibit a transition from a state in which the thermal boundary layer (BL) is nested inside the momentum BL to the one with the thermal BL being thicker than the momentum BL. The observed optimal transport enhancement is explained through an optimal coupling between the suction of hot or fresh fluid and the corresponding scalar fluctuations.

Comparative Experimental Study of Fixed Temperature and Fixed Heat Flux Boundary Conditions in Turbulent Thermal Convection.

We report the first experimental study of the influences of the thermal boundary condition on turbulent thermal convection. Two configurations were examined: one had a constant heat flux at the bottom boundary and a constant temperature at the top (CFCT cell); the other had constant temperatures at both boundaries (CTCT cell). In addition to producing different temperature stability in the boundary layers, the differences in the boundary condition lead to rather unexpected changes in the flow dynamics. It is found that, surprisingly, reversals of the large-scale circulation occur more frequently in the CTCT cell than in the CFCT cell, despite the fact that in the former its flow strength is on average 9% larger than that in the latter. Our results not only show which aspects of the thermal boundary condition are important in thermal turbulence, but also reveal that, counterintuitively, the stability of the flow is not directly coupled to its strength.

Condensation of Coherent Structures in Turbulent Flows.

Coherent structures are ubiquitous in turbulent flows and play a key role in transport. The most important coherent structures in thermal turbulence are plumes. Despite being the primary heat carriers, the potential of manipulating thermal plumes to transport more heat has been overlooked so far. Unlike some other forms of energy transport, such as electromagnetic or sound waves, heat flow in fluids is generally difficult to manipulate, as it is associated with the random motion of molecules and atoms. Here we report how a simple geometrical confinement can lead to the condensation of elementary plumes. The result is the formation of highly coherent system-sized plumes and the emergence of a new regime of convective thermal turbulence characterized by universal temperature profiles and significantly enhanced heat transfer. It is also found that the universality of the temperature profiles and heat transport originate from the geometrical properties of the coherent structures, i.e., the thermal plumes. Therefore, in contrast to the classical regime, boundary layers in this plume-controlled regime are being controlled, rather than controlling.

Confinement-induced heat-transport enhancement in turbulent thermal convection.

We report an experimental and numerical study of the effect of spatial confinement in turbulent thermal convection. It is found that when the width of the convection cell is narrowed, the heat-transfer efficiency increases significantly despite the fact that the overall flow is slowed down by the increased drag force from the sidewalls. Detailed experimental and numerical studies show that this enhancement is brought about by the changes in the dynamics and morphology of the thermal plumes in the boundary layers and in the large-scale flow structures in the bulk. It is found that the confined geometry produces more coherent and energetic hot and cold plume clusters that go up and down in random locations, resulting in more uniform and thinner thermal boundary layers. The study demonstrates how changes in turbulent bulk flow can influence the boundary layer dynamics and shows that the prevalent mode of heat transfer existing in larger aspect ratio convection cells, in which hot and cold thermal plumes are carried by the large-scale circulation along opposite sides of the sidewall, is not the most efficient way for heat transport.

Tuning heat transport via coherent structure manipulation: recent advances in thermal turbulence.

Tuning transport properties through the manipulation of elementary structures has achieved great success in many areas, such as condensed matter physics. However, the ability to manipulate coherent structures in turbulent flows is much less explored. This article reviews a recently discovered mechanism of tuning turbulent heat transport via coherent structure manipulation. We first show how this mechanism can be realized by applying simple geometrical confinement to a classical thermally driven turbulence, which leads to the condensation of elementary coherent structures and significant heat-transport enhancement, despite the resultant slower flow. Some potential applications of this new paradigm in passive heat management are also discussed. We then explain how the heat transport behaviors in seemingly different turbulence systems can be understood by this unified framework of coherent structure manipulation. Several future directions in this research area are also outlined.

Local energy dissipation rate balances local heat flux in the center of turbulent thermal convection.

The local kinetic energy dissipation rate ε(u,c) in Rayleigh-Bénard convection cell was measured experimentally using the particle tracking velocimetry method, with varying Rayleigh number Ra, Prandtl number Pr, and cell height H. It is found that ε(u,c)/(κ(3)H(-4))=1.05×10(-4)Ra(1.55±0.02)Pr(1.15±0.38). The Ra and H dependencies of the measured results are found to be consistent with the assumption made for the bulk energy dissipation rate ε(u,bulk) in the Grossmann-Lohse model. A remarkable finding of the study is that ε(u,c) balances the directly measured local Nusselt number Nu(c) in the cell center, not only scalingwise but also in magnitude.

Inverse centrifugal effect induced by collective motion of vortices in rotating thermal convection.

When a fluid system is subject to strong rotation, centrifugal fluid motion is expected, i.e., denser (lighter) fluid moves outward (inward) from (toward) the axis of rotation. Here we demonstrate, both experimentally and numerically, the existence of an unexpected outward motion of warm and lighter vortices in rotating thermal convection. This anomalous vortex motion occurs under rapid rotations when the centrifugal buoyancy is sufficiently strong to induce a symmetry-breaking in the vorticity field, i.e., the vorticity of the cold anticyclones overrides that of the warm cyclones. We show that through hydrodynamic interactions the densely distributed vortices can self-aggregate into coherent clusters and exhibit collective motion in this flow regime. Interestingly, the correlation of the vortex velocity fluctuations within a cluster is scale-free, with the correlation length being proportional ( ≈ 30%) to the cluster length. Such long-range correlation leads to the counterintuitive collective outward motion of warm vortices. Our study brings insights into the vortex dynamics that are widely present in nature.

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

We report measurements of the instantaneous viscous boundary layer (BL) thickness delta(v)(t) in turbulent Rayleigh-Bénard 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).

Universality of local dissipation scales in buoyancy-driven turbulence.

We report an experimental investigation of the local dissipation scale field eta in turbulent thermal convection. Our results reveal two types of universality of eta. The first one is that, for the same flow, the probability density functions (PDFs) of eta are insensitive to turbulent intensity and large-scale inhomogeneity and anisotropy of the system. The second is that the small-scale dissipation dynamics in buoyancy-driven turbulence can be described by the same models developed for homogeneous and isotropic turbulence. However, the exact functional form of the PDF of the local dissipation scale is not universal with respect to different types of flows, but depends on the integral-scale velocity boundary condition, which is found to have an exponential, rather than Gaussian, distribution in turbulent Rayleigh-Bénard convection.

Flow reversals in thermally driven turbulence.

We analyze the reversals of the large-scale flow in Rayleigh-Bénard convection both through particle image velocimetry flow visualization and direct numerical simulations of the underlying Boussinesq equations in a (quasi-) two-dimensional, rectangular geometry of aspect ratio 1. For medium Prandtl number there is a diagonal large-scale convection roll and two smaller secondary rolls in the two remaining corners diagonally opposing each other. These corner-flow rolls play a crucial role for the large-scale wind reversal: They grow in kinetic energy and thus also in size thanks to plume detachments from the boundary layers up to the time that they take over the main, large-scale diagonal flow, thus leading to reversal. The Rayleigh vs Prandtl number space is mapped out. The occurrence of reversals sensitively depends on these parameters.

Vortices as Brownian particles in turbulent flows.

Brownian motion of particles in fluid is the most common form of collective behavior in physical and biological systems. Here, we demonstrate through both experiment and numerical simulation that the movement of vortices in a rotating turbulent convective flow resembles that of inertial Brownian particles, i.e., they initially move ballistically and then diffusively after certain critical time. Moreover, the transition from ballistic to diffusive behaviors is direct, as predicted by Langevin, without first going through the hydrodynamic memory regime. The transitional timescale and the diffusivity of the vortices can be collapsed excellently onto a master curve for all explored parameters. In the spatial domain, however, the vortices exhibit organized structures, as if they are performing tethered random motion. Our results imply that the convective vortices have inertia-induced memory such that their short-term movement can be predicted and their motion can be well described in the framework of Brownian motions.

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.

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.

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.

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.