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We present an experimental study of Rayleigh-B\'enard convection using liquid metal alloy gallium-indium-tin as the working fluid with a Prandtl number of $Pr=0.029$. The flow state and the heat transport were measured in a Rayleigh number range of $1.2\times10^{4} \le Ra \le 1.3\times10^{7}$. The temperature fluctuation at the cell centre is used as a proxy for the flow state. It is found that, as $Ra$ increases from the lower end of the parameter range, the flow evolves from a convection state to an oscillation state, a chaotic state, and finally a turbulent state for $Ra>10^5$. The study suggests that the large-scale circulation in the turbulent state is a residual of the cell structures near the onset of convection, which is in contrast with the case of $Pr\sim1$, where the cell structure is replaced by high-order flow modes transiently before the emergence of the large-scale circulation in the turbulent state. The evolution of the flow state is also reflected by the heat transport characterised by the Nusselt number $Nu$ and the probability density function (PDF) of the temperature fluctuation at the cell centre. It is found that the effective local heat transport scaling exponent $\gamma$, i.e., $Nu\sim Ra^{\gamma}$, changes continuously from $\gamma=0.49$ at $Ra\sim 10^4$ to $\gamma=0.25$ for $Ra>10^6$. Meanwhile, the PDF at the cell centre gradually evolves from a Gaussian-like shape before the transition to turbulence to an exponential-like shape in the turbulent state. For $Ra>10^6$, the flow shows self-similar behaviour, which is revealed by the universal shape of the PDF of the temperature fluctuation at the cell centre and a $Nu=0.19Ra^{0.25}$ scaling for the heat transport., Comment: 12 pages, 5 figures; Accepted for publication in the Journal of Fluid Mechanics

We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh-B\'enard convection in a reduced Rayleigh-number range $1.3{\le}Ra/Ra_{c}{\le}166$. Under slow rotations ($Ra{\gtrsim}10Ra_{c}$), the vortices are randomly distributed. The size-distribution of the Voronoi cells of the vortex centers is well described by the standard $\Gamma$ distribution. In this flow regime the vortices exhibit Brownian-type horizontal motion. The probability density functions of the vortex displacements are, however, non-Gaussian at short time scales. At modest rotating rates ($4Ra_{c}{\le}Ra{\lesssim}10Ra_{c}$) the centrifugal force leads to radial vortex motions, i.e., warm cyclones (cold anticyclones) moving towards (outward from) the rotation axis. The mean-square-displacements of the vortices increase faster than linearly at large time. This super-diffusive behavior can be satisfactorily explained by a Langevin model incorporating the centrifugal force. In the rapidly rotating regime ($1.6Ra_{c}{\le}Ra{\le}4Ra_{c}$) the vortices are densely distributed, with the size-distribution of their Voronoi cells differing significantly from the standard $\Gamma$ distribution. The hydrodynamic interaction of neighboring vortices results in formation of vortex clusters. Inside clusters the correlation of the vortex velocity fluctuations is scale free, with the correlation length being approximately $30\%$ of the cluster length. We examine the influence of cluster forming on the dynamics of individual vortex. Within clusters, cyclones exhibit inverse-centrifugal motion as they submit to the motion of strong anticyclones, while the velocity for outward motion of the anticyclones is increased. Our analysis show that the mobility of isolated vortices, scaled by their vorticity strength, is a simple power function of the Froude number.

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 turbulent 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 populated 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 about 30% of the cluster length. Such long-range correlation leads to the collective outward motion of cyclones. Our study provides new understanding of vortex dynamics that are widely present in nature.

We present high-precision experimental and numerical studies of the Nusselt number $Nu$ as functions of the Rayleigh number $Ra$ in geostrophic rotating convection with domain aspect ratio ${\Gamma}$ varying from 0.4 to 3.8 and the Ekman number Ek from $2.0{\times}10^{-7}$ to $2.7{\times}10^{-5}$. The heat-transport data $Nu(Ra)$ reveal a gradual transition from buoyancy-dominated to geostrophic convection at large $Ek$, whereas the transition becomes sharp with decreasing $Ek$. We determine the power-law scaling of $Nu{\sim}Ra^{\gamma}$, and show that the boundary flows give rise to pronounced enhancement of $Nu$ in a broad range of the geostrophic regime, leading to reduction of the scaling exponent ${\gamma}$ in small ${\Gamma}$ cells. The present work provides new insight into the heat-transport scaling in geostrophic convection and may explain the discrepancies observed in previous studies., Comment: 5 pages, 4 figures, 1 table

We present an investigation of the root-mean-square (rms) temperature $\sigma_T$ and the rms velocity $\sigma_w$ in the bulk of Rayleigh-B\'enard turbulence, using new experimental data from the current study and experimental and numerical data from previous studies. We find that, once scaled by the convective temperature $\theta_*$, the value of $\sigma_T$ at the cell centre is a constant, i.e. $\sigma_{T,c}/\theta_* \approx 0.85$, over a wide range of the Rayleigh number ($10^{8}\leq Ra\leq 10^{15}$) and the Prandtl number ($0.7\leq Pr \leq 23.34$), and is independent of the surface topographies of the top and bottom plates of the convection cell. A constant close to unity suggests that $\theta_*$ is a proper measure of the temperature fluctuation in the core region. On the other hand, $\sigma_{w,c}/w_*$, the vertical rms velocity at the cell centre scaled by the convective velocity $w_*$, shows a weak $Ra$-dependence ($\sim Ra^{0.07\pm0.02}$) over $10^8\leq Ra\leq 10^{10}$ at $Pr\sim4.3$ and is independent of plate topography. Similar to a previous finding by He \& Xia ({\it Phys. Rev. Lett.,} vol. 122, 2019, 014503), we find that the rms temperature profile $\sigma_T(z)/\theta_*$ in the region of the mixing zone with a mean horizontal shear exhibits a power-law dependence on the distance $z$ from the plate, but now the universal profile applies to both smooth and rough surface topographies and over a wider range of $Ra$. The vertical rms velocity profile $\sigma_w(z)/w_*$ obey a logarithmic dependence on $z$. The study thus demonstrates that the typical scales for the temperature and the velocity are the convective temperature $\theta_*$ and the the convective velocity $w_*$, respectively. Finally, we note that $\theta_*$ may be utilised to study the flow regime transitions in the ultra-high-$Ra$-number turbulent convection., Comment: 12 pages, 6 figures; Accepted for publication in the Journal of Fluid Mechanics

In rotating Rayleigh-B\'enard convection, columnar vortices advect horizontally in a stochastic manner. When the centrifugal buoyancy is present the vortices exhibit radial motions that can be explained through a Langevin-type stochastic model. Surprisingly, anomalous outward motion of cyclones is observed in a centrifugation-dominant flow regime, which is contrary to the well-known centrifugal effect. We interpret this phenomenon as a symmetry-breaking of both the population and vorticity magnitude of the vortices brought about by the centrifugal buoyancy. Consequently, the cyclones submit to the collective vortex motion dominated by the strong anticyclones. Our study provides new understanding of vortex motions that are widely present in many natural systems.

Vortices play an unique role in heat and momentum transports in astro- and geo-physics, and it is also the origin of the Earth's dynamo. A question existing for a long time is whether the movement of vortices can be predicted or understood based on their historical data. Here we use both the experiments and numerical simulations to demonstrate some generic features of vortex motion and distribution. It can be found that the vortex movement can be described on the framework of Brownian particles where they move ballistically for the time shorter than some critical timescales, and then move diffusively. Traditionally, the inertia of vortex has often been neglected when one accounts for their motion, our results imply that vortices actually have inertial-induced memory such that their short term movement can be predicted. Extending to astro- and geo-physics, the critical timescales of transition are in the order of minutes for vortices in atmosphere and ocean, in which this inertial effect may often be neglected compared to other steering sources. However, the timescales for vortices are considerably larger which range from days to a year. It infers the new concept that not only the external sources alone, for example the solar wind, but also the internal source, which is the vortex inertia, can contribute to the short term Earth's magnetic field variation., Comment: 9 pages, 4 figures

We present a numerical study of quasistatic magnetoconvection in a cubic Rayleigh-B\'enard (RB) convection cell subjected to a vertical external magnetic field. For moderate values of the Hartmann number Ha, we find an enhancement of heat transport. Furthermore, a maximum heat transport enhancement is observed at certain optimal $Ha_{opt}$. The enhanced heat transport may be understood as a result of the increased coherency of the thermal plumes, which are elementary heat carriers of the system. To our knowledge this is the first time that a heat transfer enhancement by the stabilising Lorentz force in quasistatic magnetoconvection has been observed. We further found that the optimal enhancement may be understood in terms of the crossing between the thermal and the momentum boundary layers (BL) and the fact that temperature fluctuations are maximum near the position where the BLs cross. These findings demonstrate that the heat transport enhancement phenomenon in the quasistatic magnetoconvection system belongs to the same universality class of stabilising$-$destabilising ($S$-$D$) turbulent flows as the systems of confined Rayleigh-B\'enard (CRB), rotating Rayleigh-B\'enard (RRB) and double-diffusive convection (DDC). This is further supported by the findings that the heat transport, boundary layer ratio and the temperature fluctuations in magnetoconvection at the boundary layer crossing point are similar to the other three cases., Comment: 25 pages, 17 figures, submitted to Journal of Fluid Mechanics. Due to the limitation "The abstract field cannot be longer than 1,920 characters", the abstract appearing here is slightly shorter than that in the PDF file

In scalar turbulence it is sometimes the case that the scalar diffusivity is smaller than the viscous diffusivity. The thermally-driven turbulent convection in water is a typical example. In such a case the smallest scale in the problem is the Batchelor scale $l_b$, rather than the Kolmogorov scale $l_k$, as $l_b = l_k/Sc^{1/2}$, where Sc is the Schmidt number (or Prandtl number in the case of temperature). In the numerical studies of such scalar turbulence, the conventional approach is to use a single grid for both the velocity and scalar fields. Such single-resolution scheme often over-resolves the velocity field because the resolution requirement for scalar is higher than that for the velocity field, since $l_b1$. In this paper we put forward an algorithm that implements the so-called multiple-resolution method with a finite-volume code. In this scheme, the velocity and pressure fields are solved in a coarse grid, while the scalar field is solved in a dense grid. The central idea is to implement the interpolation scheme on the framework of finite-volume to reconstruct the divergence-free velocity from the coarse to the dense grid. We demonstrate our method using a canonical model system of fluid turbulence, the Rayleigh-B\'enard convection. We show that, with the tailored mesh design, considerable speed-up for simulating scalar turbulence can be achieved, especially for large Schmidt (Prandtl) numbers. In the same time, sufficient accuracy of the scalar and velocity fields can be achived by this multiple-resolution scheme. Although our algorithm is demonstrated with a case of an active scalar, it can be readily applied to passive scalar turbulent flows., Comment: 16 pages, 11 figures, submitted to Journal of Computational Physics

We study, using direct numerical simulations, the effect of geometrical confinement on heat transport and flow structure in Rayleigh-B\'enard convection in fluids with different Prandtl numbers. Our simulations span over two decades of Prandtl number $Pr$, $0.1 \leq Pr \leq 40$, with the Rayleigh number $Ra$ fixed at $10^8$. The width-to-height aspect ratio $\Gamma$ spans between $0.025$ and $0.25$ while the length-to-height aspect ratio is fixed at one. We first find that for $Pr \geq 0.5$, geometrical confinement can lead to a significant enhancement in heat transport as characterized by the Nusselt number $Nu$. For those cases, $Nu$ is maximal at a certain $\Gamma = \Gamma_{opt}$. It is found that $\Gamma_{opt}$ exhibits a power-law relation with $Pr$ as $\Gamma_{opt}=0.11Pr^{-0.06}$, and the maximal relative enhancement generally increases with $Pr$ over the explored parameter range. As opposed to the situation of $Pr \geq 0.5$, confinement-induced enhancement in $Nu$ is not realized for smaller values of $Pr$, such as $0.1$ and $0.2$. The $Pr$ dependence of the heat transport enhancement can be understood in its relation to the coverage area of the thermal plumes over the thermal boundary layer (BL) where larger coverage is observed for larger $Pr$ due to a smaller thermal diffusivity. We further show that $\Gamma_{opt}$ is closely related to the crossing of thermal and momentum BLs, and find that $Nu$ declines sharply when the thickness ratio of the thermal and momentum BLs exceeds a certain value of about one. In addition, through examining the temporally averaged flow fields and 2D mode decomposition, it is found that for smaller $Pr$ the large-scale circulation is robust against the geometrical confinement of the convection cell., Comment: 25 pages, 11 figures, and 1 table in main text

We present a systematic investigation of the effects of roughness geometry on turbulent Rayleigh-B\'enard convection (RBC) over rough plates with pyramid-shaped and periodically distributed roughness elements. Using a parameter $\lambda$ defined as the height of a roughness element over its base width, the heat transport, the flow dynamics and local temperatures are measured for the Rayleigh number range $7.50\times 10^{7} \leq Ra\leq 1.31\times 10^{11}$, and the Prandtl number $Pr$ from 3.57 to 23.34 at four values of $\lambda$. It is found that the heat transport scaling, i.e. $Nu\sim Ra^{\alpha}$ where $Nu$ is the Nusselt number, may be classified into three regimes. In Regime I, the system is in a dynamically smooth state. The heat transport scaling is the same as that in a smooth cell. In Regimes II and III, the heat transport enhances. When $\lambda$ is increased from 0.5 to 4.0, $\alpha$ increases from 0.36 to 0.59 in Regime II, and it increases from 0.30 to 0.50 in Regime III. The experiment demonstrates the heat transport scaling in turbulent RBC can be manipulated using $\lambda$. Previous studies suggest that the transition from Regime I to Regime II, occurs when the thermal boundary layer (BL) thickness becomes smaller than the roughness height $h$. Direct measurements of the viscous BL in the present study suggest that the transition from Regime II to Regime III is likely a result of the viscous BL thickness becoming smaller $h$. The scaling exponent of the Reynolds number $Re$ vs. $Ra$ changes from 0.471 to 0.551 when $\lambda$ is increased from 0.5 to 4.0. It is also found that increasing $\lambda$ increases the clustering of thermal plumes which effectively increases the plumes lifetime that are ultimately responsible for the enhanced heat transport., Comment: 27 pages, 19 figures

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-B\'enard (RB) convection, i.e. buoyancy-driven flow with the fluid density being affected by a scalar field. In the three cases different {\it 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 {\it 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 organised 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., Comment: 10 pages, 5 figures, and 3 tables in main text and supplementary materials

The effects of insulating lids on the convection beneath were investigated experimentally using rectangular convection cells in the flux Rayleigh number range $2.3\times10^{9}\leq Ra_F \leq 1.8\times10^{11}$ and cylindrical cells in the range $1.4\times10^{10}\leq Ra_F \leq 1.2\times10^{12}$ with the Prandtl number Pr fixed at 4.3. It is found that the presence of the insulating lids leads to reduction of the global heat transfer efficiency as expected, which primarily depends on the insulating area but is insensitive to the detailed insulating patterns. At the leading order level, the magnitude of temperature fluctuation in the bulk fluid is, again, found to be insensitive to the insulating pattern and mainly depends on the insulating area; while the temperature probability density function (PDF) in the bulk is essentially invariant with respect to both insulating area and the spatial pattern of the lids. The flow dynamics, on the other hand, is sensitive to both the covering area and the spatial distribution of the lids. At fixed $Ra_F$, the flow strength is found to increase with increasing insulating area so as to transfer the same amount of heat through a smaller cooling area. Moreover, for a constant insulating area, a symmetric insulating pattern results in a symmetric flow pattern, i.e. double-roll structure; whereas asymmetric insulating pattern leads to asymmetric flow, i.e. single-roll structure. It is further found that the symmetry breaking of the insulating pattern leads to a stronger flow that enhances the horizontal velocity more than the vertical one., Comment: Submited to JFM

We present an experimental investigation of the dynamics and flow-coupling of convective turbulent flows in a cylindrical Rayleigh-Benard convection cell with two immiscible fluids, water and fluorinert FC-77 electronic liquid (FC77). It is found that one large-scale circulation (LSC) roll exists in each of the fluid layers, and that their circulation planes have two preferred azimuthal orientations separated by $\sim\pi$. A surprising finding of the study is that cessations/reversals of the LSC in FC77 of the two-layer system occur much more frequently than they do in single-layer turbulent RBC, and that a cessation is most likely to result in a flow reversal of the LSC, which is in sharp contrast with the uniform distribution of the orientational angular change of the LSC before and after cessations in single-layer turbulent RBC. This implies that the dynamics governing cessations and reversals in the two systems are very different. Two coupling modes, thermal coupling (flow directions of the two LSCs are opposite to each other at the fluid-fluid interface) and viscous coupling (flow directions of the two LSCs are the same at the fluid-fluid interface), are identified with the former one as the predominant mode. That most cessations (in the FC77 layer) end up as reversals can be understood as a symmetry breaking imposed by the orientation of the LSC in the water layer, which remained unchanged most of the time. Furthermore, the frequently occurring cessations and reversals are caused by the system switching between its two metastable states, i.e. thermal and viscous coupling modes. It is also observed that the strength of the LSC in water becomes weaker when the LSC in FC77 rotates faster azimuthally and that the flow strength in FC77 becomes stronger when the LSC in water rotates faster azimuthally, i.e. the influence of the LSC in one fluid layer on the other is not symmetric., Comment: 13 pages, 8 figures

We present experimental evidence that a minute amount of polymer additives can significantly enhance heat transport in the bulk region of turbulent thermal convection. The effects of polymer additives are found to be the \textit{suppression} of turbulent background fluctuations that give rise to incoherent heat fluxes that make no net contribution to heat transport, and at the same time to \textit{increase} the coherency of temperature and velocity fields. The suppression of small-scale turbulent fluctuations leads to more coherent thermal plumes that result in the heat transport enhancement. The fact that polymer additives can increase the coherency of thermal plumes is supported by the measurements of a number of local quantities, such as the extracted plume amplitude and width, the velocity autocorrelation functions and the velocity-temperature cross-correlation coefficient. The results from local measurements also suggest the existence of a threshold value for the polymer concentration, only above which can significant modification of the plume coherent properties and enhancement of the local heat flux be observed. Estimation of the plume emission rate suggests that the second effect of polymer additives is to stabilize the thermal boundary layers., Comment: 8 figures, 11 pages

We report an experimental study of the properties of the velocity boundary layer in turbulent Rayleigh-B\'{e}nard convection in a cylindrical cell. The measurements were made at Rayleigh numbers $Ra$ in the range $2.8\times10^{8}

We examine the behavior of the Kolmogorov constants C_2, C_k, and C_{k1}, which are, respectively, the prefactors of the second order longitudinal structure function, the three dimensional and one-dimensional longitudinal energy spectrum in the inertial range. We show that their ratios, C_2/C_{k1} and C_k/C_{k1}, exhibit clear dependence on the micro-scale Reynolds number R_{\lambda}, implying that they cannot all be independent of R_{\lambda}. In particular, it is found that (C_{k1}/C_2-0.25) = 1.95R_{\lambda}^{-0.68}. The study further reveals that the widely-used relation C_2 = 4.02 C_{k1} holds only asymptotically when R_{\lambda} <= 10^5. It is also found that C_2 has much stronger R_{\lambda}-dependence than either C_k, or C_{k1} if the latter indeed has a systematic dependence on R_{\lambda}. We further show that the variable dependence on R_{\lambda} of these three numbers can be attributed to the difference of the inertial range in real- and wavenumber-space, with inertial range in real-space known to be much shorter than that in wavenumber space., Comment: 10 pages, 4 figures. Journal of Fluid Mechanics format (JFM.cls)

We report an experimental investigation of pair dispersions in turbulent thermal convection with initial separation r0 ranging from sub-Kolmogorov scale to scales in the inertial range. In the dissipative range of scales we observed for the first time in experiment the exponential growth of the separation between a pair of particles predicted by Batchelor and obtained a Batchelor constant 0.23\pm0.07. For large r0, it is found that, for almost all time range, both the mean-square separation and distance neighbor function exhibit the forms predicted by Batchelor, whereas the two quantities agree with Richardson's predictions for small r0. Moreover, the measured value of the Richardson constant g = 0.10 \pm 0.07, which is smaller than those found in other turbulence systems. We also demonstrate the crossover of the mean-square separation from the exponential to the Batchelor regimes in both temporal and spatial scales., Comment: 5 pages, 4 figures

We numerically investigate the structures of the near-plate temperature profiles close to the bottom and top plates of turbulent Rayleigh-B\'{e}nard flow in a cylindrical sample at Rayleigh numbers Ra=10^8 to Ra=2\times10^{12} and Prandtl numbers Pr=6.4 and Pr=0.7 with the dynamical frame method [Q. Zhou and K.-Q. Xia, Phys. Rev. Lett. 104, 104301 (2010)] thus extending previous results for quasi-2-dimensional systems to 3D systems for the first time. The dynamical frame method shows that the measured temperature profiles in the spatially and temporally local frame are much closer to the temperature profile of a laminar, zero-pressure gradient boundary layer according to Pohlhausen than in the fixed reference frame. The deviation between the measured profiles in the dynamical reference frame and the laminar profiles increases with decreasing Pr, where the thermal BL is more exposed to the bulk fluctuations due to the thinner kinetic BL, and increasing Ra, where more plumes are passing the measurement location., Comment: 5 pages, 2 figures

We analyze the reversals of the large scale flow in Rayleigh-B\'enard convection both through particle image velocimetry flow visualization and direct numerical simulations (DNS) 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. Based on this mechanism we identify a typical time scale for the reversals. We map out the Rayleigh number vs Prandtl number phase space and find that the occurrence of reversals very sensitively depends on these parameters., Comment: 4 pages, 4 figures

We investigate the structures of the near-plate velocity and temperature profiles at different horizontal positions along the conducting bottom (and top) plate of a Rayleigh-B\'{e}nard convection cell, using two-dimensional (2D) numerical data obtained at the Rayleigh number Ra=10^8 and the Prandtl number Pr=4.4 of an Oberbeck-Boussinesq flow with constant material parameters. The results show that most of the time, and for both velocity and temperature, the instantaneous profiles scaled by the dynamical frame method [Q. Zhou and K.-Q. Xia, Phys. Rev. Lett. 104, 104301 (2010) agree well with the classical Prandtl-Blasius laminar boundary layer (BL) profiles. Therefore, when averaging in the dynamical reference frames, which fluctuate with the respective instantaneous kinematic and thermal BL thicknesses, the obtained mean velocity and temperature profiles are also of Prandtl-Blasius type for nearly all horizontal positions. We further show that in certain situations the traditional definitions based on the time-averaged profiles can lead to unphysical BL thicknesses, while the dynamical method also in such cases can provide a well-defined BL thickness for both the kinematic and the thermal BLs., Comment: 16 pages, 16 figures

We present a method of disentangling the anisotropies produced by the cliff structures in turbulent velocity field and test it in the system of turbulent Rayleigh-B\'{e}nard (RB) convection. It is found that in the RB system the cliff structures in the velocity field are generated by thermal plumes. These cliff structures induce asymmetry in the velocity increments, which leads us to consider the plus and minus velocity structure functions (VSF). The plus velocity increments exclude cliff structures, while the minus ones include them. Our results show that the scaling exponents of the plus VSFs are in excellent agreement with those predicted for homogeneous and isotropic turbulence (HIT), whereas those of the minus VSFs exhibit significant deviations from HIT expectations in places where thermal plumes abound. These results demonstrate that plus and minus VSFs can be used to quantitatively study the effect of cliff structures in the velocity field and to effectively disentangle the associated anisotropies caused by these structures., Comment: 10 pages, 5 figures

We present a systematic experimental study of geometric and statistical properties of thermal plumes in turbulent Rayleigh-B\'{e}nard convection using the thermochromic-liquid-crystal (TLC) technique. The experiments were performed in three water-filled cylindrical convection cells with aspect ratios 2, 1, and 0.5 and over the Rayleigh-number range $5\times10^7 \leq Ra \leq 10^{11}$. TLC thermal images of horizontal plane cuts at various depths below the top plate were acquired. Three-dimensional images of thermal plumes were then reconstructed from the two-dimensional slices of the temperature field. The results show that the often-called sheetlike plumes are really one-dimensional structures and may be called rodlike plumes. We find that the number densities for both sheetlike/rodlike and mushroomlike plumes have power-law dependence on $Ra$ with scaling exponents of $\sim 0.3$, which is close to that between the Nusselt number $Nu$ and $Ra$. This result suggests that it is the plume number that primarily d ermines the scaling exponent of the $Nu$-$Ra$ scaling relation. The evolution of the aspect ratio of sheetlike/rodlike plumes reveals that as $Ra$ increases the plume geometry changes from more-elongated to less-elongated. Our study of the plume area fraction (fraction of coverage over the surface of the plate) further reveals that the increased plume numbers with $Ra$ mainly comes from increased plume emission, rather than fragmentation of plumes. In addition, the area, perimeter, and the shape complexity of the two-dimensional horizontal cuts of sheetlike/rodlike plumes were studied and all are found to obey log-normal distributions., Comment: 22 pages, 16 figures, submitted to the New Journal of Physics

The shape of velocity and temperature profiles near the horizontal conducting plates in turbulent Rayleigh-B\'{e}nard convection are studied numerically and experimentally over the Rayleigh number range $10^8\lesssim Ra\lesssim3\times10^{11}$ and the Prandtl number range $0.7\lesssim Pr\lesssim5.4$. The results show that both the temperature and velocity profiles well agree with the classical Prandtl-Blasius laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses., Comment: 10 pages, 6 figures

We report measurements of the instantaneous viscous boundary layer (BL) thickness $\delta_v(t)$ in turbulent Rayleigh-B\'{e}nard 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 $\delta_v(t)$., Comment: 5 pages, 5 figures, Accepted for publication in Phys. Rev. Lett

We report an experimental study of the large-scale circulation (LSC) in a turbulent Rayleigh-B\'{e}nard convection cell with aspect ratio unity. The temperature-extremum-extraction (TEE) method for obtaining the dynamic information of the LSC is presented. With this method, the azimuthal angular positions of the hot ascending and cold descending flows along the sidewall are identified from the measured instantaneous azimuthal temperature profile. The motion of the LSC is then decomposed into two different modes: the azimuthal mode and the translational or off-center mode. Comparing to the previous sinusoidal-fitting (SF) method, it is found that both methods give the same information about the azimuthal motion of the LSC, but the TEE method in addition can provide information about the off-center motion of the LSC, which is found to oscillate time-periodically around the cell's central vertical axis with an amplitude being nearly independent of the turbulent intensity. It is further found that the azimuthal angular positions of the hot ascending flow near the bottom plate and the cold descending flow near the top plate oscillate periodically out of phase by $\pi$, leading to the torsional mode of the LSC. These oscillations are then propagated vertically along the sidewall by the hot ascending and cold descending fluids. When they reach the mid-height plane, the azimuthal positions of the hottest and coldest fluids again oscillate out of phase by $\pi$. It is this out-of-phase horizontal positional oscillation of the hottest and coldest fluids at the same horizontal plane that produces the off-center oscillation of the LSC. A direct velocity measurement further confirms the existence of the bulk off-center mode of the flow field near cell center., Comment: 13 pages, 14 figures, the paper has been submitted to J. Fluid Mech

We report an experimental study of the three-dimensional spatial structure of the low frequency temperature oscillations in a cylindrical Rayleigh-B\'{e}nard convection cell. It is found that thermal plumes are not emitted periodically, but randomly and continuously, from the top and bottom plates. We further found that the oscillation of the temperature field does not originate from the boundary layers, but rather is a result of the horizontal motion of the hot ascending and cold descending fluids being modulated by the twisting and sloshing motion of the bulk flow field., Comment: 5 figures

We investigate experimentally the statistical properties of active and passive scalar fields in turbulent Rayleigh-B\'{e}nard convection in water, at $Ra\sim10^{10}$. 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., Comment: 13 pages and 12 figures

Temperature and velocity oscillations have been found in a rectangular Rayleigh-B\'{e}nard convection cell, in which one large scale convection roll exists. At $Ra=8.9 \times 10^{11}$ and $Pr=4$, temperature oscillation can be observed in most part of the system and the oscillation period remains almost constant, $t_T = 74 \pm 2$ seconds. Velocity oscillation can only be found in its horizontal component, $v_y$ (perpendicular to large scale circulation plane), near the cell sidewall, its oscillation period is also constant, $t_T = 65 \pm 2$ seconds, at these positions. Temperature and velocity oscillations have different Ra dependence, which are respectively indicated by Peclect number $Pe_T = 0.55Ra^{0.47}$ and $Pe_v = 0.28Ra^{0.50}$ . In comparison to the case of cylindrical cell, we find that the velocity oscillation is affected by the system geometry., Comment: 6 pages, 6 figures. submitted to PRE

We present a scheme to extract information about plumes, a prominent coherent structure in turbulent thermal convection, from simultaneous local velocity and temperature measurements. Using this scheme, we study the temperature dependence of the plume velocity and understand the results using the equations of motion. We further obtain the average local heat flux in the vertical direction at the cell center. Our result shows that heat is not mainly transported through the central region but instead through the regions near the sidewalls of the convection cell., Comment: 4 pages, 4 figures, submitted to Physical Review Letters