We report a numerical investigation of a previously noticed but less explored flow state transition in two-dimensional turbulent Rayleigh–Bénard convection. The simulations are performed in a square domain over a Rayleigh number range of $10^7 \leq Ra \leq 2 \times 10^{11}$ and a Prandtl number range of $0.25 \leq Pr \leq 20$. The transition is characterized by the emergence of multiple satellite eddies with increasing $Ra$, which orbit around and interact with the main vortex roll in the system. Consequently, the main roll is squeezed to a smaller size compared with the domain and wanders around in the bulk region irregularly and extensively. This is in sharp contrast to the flow state before the transition, which is featured by a domain-sized circulatory roll with its vortex centre ‘condensed’ near the domain's centre. Detailed velocity field analysis reveals that there exists an abrupt increase in the energy fluctuations of the Fourier modes during the transition. Based on this phase-transition-like signal, the critical condition for the transition is found to follow a scaling relation as $Ra_t \sim Pr^{1.41}$ where $Ra_t$ is the critical Rayleigh number for the transition. This scaling relation is quantitatively explained by a phenomenological model grounded on the bistability behaviour (i.e. spontaneous and stochastic switching between the two flow states) observed at the edge of the transition. The model can also account for the effects of aspect ratio on the transition reported in the literature (van der Poel et al., Phys. Fluids, vol. 24, 2012).

We report an experimental study of the formation and evolution of laminar thermal structures generated by a small heat source, with a focus on their correlation to the thermal boundary layer and effects of heating time $t_{heat}$. The experiments are performed over the flux Rayleigh number ($Ra_f$) range $2.1\times 10^6 \leq Ra_f \leq 3.6\times 10^{7}$ and the Prandtl number ($Pr$) range $28.6 \leq Pr \leq 904.7$. The corresponding Rayleigh number ($Ra= t_{heat}\,Ra_{f}/\tau _0\,Pr$) range is $900 \leq Ra \leq 4\times 10^{4}$, where $\tau _0$ is a diffusion time scale. For thermal structures generated by continuous heating (i.e. starting plumes), their formation process exists three characteristic times that are well reflected by changes in the thermal boundary layer thickness. These characteristic times, denoted as $t_{emit}$, $t_{recover}$ and $t_{static}$, correspond to the moments when the plume emission begins and completes, and when the thermal boundary layer becomes quasi-static, respectively. Their $Ra_f$–$Pr$ dependencies are found to be $t_{emit}/\tau _0\sim Ra_f^{-0.41}\,Pr^{0.41}$, $t_{recover}/\tau _0\sim Ra_f^{-0.48}\,Pr^{0.48}$ and $t_{static}/\tau _0\sim Ra_f^{-0.49}\,Pr^{0.33}$, respectively. Thermal structures generated by finite $t_{heat}$ exhibit similar evolution dynamics once $t_{heat} \ge t_{emit}$, with the accelerating stage behaving like starting plumes and the decay stage like thermals (i.e. a finite amount of buoyant fluids). It is further found that their maximum rising velocity experiences a transition in the $Ra$-dependence from $Ra$ to $(Ra\ln Ra)^{0.5}$ at $Ra \simeq 6000$; and their maximum acceleration reaches the value of starting plumes at $t_{heat}\simeq t_{recover}$, and remains unchanged for larger $t_{heat}$. In particular, the maximum rising velocity for the cases with $t_{heat} = t_{recover}$ follows a scaling relation $Ra_f^{0.37}\,Pr^{-0.37}$, in contrast to the relation $Ra_f^{0.48}\,Pr^{-0.48}$ for starting plumes. This study provides a more comprehensive understanding of laminar thermal structures, which are relevant to a range of processes in nature and laboratory systems such as Rayleigh–Bénard convection.

The existence of Bolgiano–Obukhov (BO) scaling in Rayleigh–Bénard convection (RBC) has long been speculated. However, due to the inhomogeneity and anisotropy of the flow, and the lack of clear scale separation, no conclusive evidence has been found. To avoid these non-ideal factors, we construct an idealized isotropic convection system by introducing an additional horizontal buoyancy field to RBC in a doubly periodic domain. We focus on the two-dimensional case so that its upscale kinetic energy flux can enable a long inertial range for detecting the BO scaling. Through direct numerical simulations of this system, we justify the existence of BO scaling using second- and third-order structure functions, which are in good agreement with our theoretically obtained scaling relations from the Kármán–Howarth–Monin equations. These theoretical and numerical results provide direct support for the conjecture that the existence of the BO scaling in RBC is associated with the inverse kinetic energy cascade. For higher-order structure functions, we found strong intermittent effects in the buoyancy field, but not in the velocity. By comparing the present system with the canonical anisotropic RBC in a periodic domain, the effects of anisotropy on the scaling properties are elucidated.

We report a direct numerical simulation (DNS) study of the mean velocity and temperature profiles in turbulent Rayleigh–Bénard convection (RBC) at low Prandtl numbers ($Pr$). The numerical study is conducted in a vertical thin disk with $Pr$ varied in the range $0.17\leq Pr\leq 4.4$ and the Rayleigh number ($Ra$) varied in the range $5\times 10^8\leq Ra \leq 1\times 10^{10}$. By varying $Pr$ from 4.4 to 0.17, we find a sharp change of flow patterns for the large-scale circulation (LSC) from a rigid-body rotation to a near-wall turbulent jet. We numerically examine the mean velocity equation in the bulk region and find that the mean horizontal velocity profile $u(z)$ can be determined by a balance equation between the mean convection and turbulent diffusion with a constant turbulent viscosity $\nu _t$. This balance equation admits a self-similarity jet solution, which fits the DNS data well. In the boundary-layer region, we find that both the mean temperature profile $T(z)$ and $u(z)$ can be determined by a balance equation between the molecular diffusion and turbulent diffusion. Within the viscous boundary layer, both $u(z)$ and $T(z)$ can be solved analytically and the analytical results agree well with the DNS data. Our careful characterisation of the mean velocity and temperature profiles in low-$Pr$ RBC provides a further understanding of the intricate interplay between the LSC, plume emission and boundary-layer dynamics, and pinpoints the physical mechanism for the emergence of a pronounced LSC in low-$Pr$ RBC.

We report an experimental study of the Prandtl-number effects in quasi-two-dimensional (quasi-2-D) Rayleigh–Bénard convection. The experiments were conducted in four rectangular convection cells over the Prandtl-number range of $11.7 \leqslant Pr \leqslant 650.7$ and over the Rayleigh-number range of $6.0\times 10^8 \leqslant Ra \leqslant 3.0\times 10^{10}$. Flow visualization reveals that, as $Pr$ increases from 11.7 to 145.7, thermal plumes pass through the central region much less frequently and their self-organized large-scale motion is more confined along the periphery of the convection cell. The large-scale flow is found to break down for higher $Pr$, resulting in a regime transition in the Reynolds number $Re$. For the $Pr$ range with a large-scale flow of system size, the $Re$ number, Nusselt number $Nu$ and local temperature fluctuations were investigated systematically. It is found that $Re$ scales as $Re \sim Ra^{0.58}Pr^{-0.82}$ in the present geometry, which suggests that it is in line with the behaviour in the 2-D configuration. On the other hand, the measured $Nu(Ra, Pr)$ relation $Nu \sim Ra^{0.289}Pr^{-0.02}$ tends to be compatible with the finding in a three-dimensional (3-D) system. For the temperature fluctuations in the cell centre and near the sidewall, they exhibit distinct $Ra$-dependent scalings that could not be accounted for with existing theories, but their $Pr$ dependences for $Pr \lesssim 50$ are in agreement with the predictions by Grossmann & Lohse (Phys. Fluids, vol. 16, 2004, pp. 4462–4472). These results enrich our understanding of quasi-2-D thermal convection, and its similarities and differences compared to 2-D and 3-D systems.

We present an experimental study of the reversal of the large-scale circulation (LSC) in quasi-two-dimensional turbulent Rayleigh–Bénard convection. It is found that there exists a transition in the Rayleigh number ($Ra$) dependence of the reversal rate $f$ with two distinct scalings: for $Ra$ less than a transitional value $Ra_{t}$, the non-dimensionalized reversal rate $ft_{E}\sim Ra^{-1.09}$; however, for higher $Ra$ the scaling changes to $ft_{E}\sim Ra^{-3.06}$, where $t_{E}$ is the turnover time of the LSC. Flow visualization shows that this regime transition originates from a change in flow topology from a single-roll state to a new, less stable, abnormal single-roll state with substructures inside the single roll. The emergence of the substructures inside the LSC lowers the energy barrier for the flow reversals to occur and leads to a slower decay of $f$ with $Ra$. Detailed analysis reveals that, although it is the corner rolls that trigger the reversal event, the probability for the occurrence of reversals mainly depends on the stability of the LSC. This is supported by a model we proposed to predict the critical condition for the transition, which agrees well with the experimental results.

The effects of insulating lids on the convection beneath were investigated experimentally using rectangular convection cells in the flux Rayleigh number range $2.3\times 10^{9}\leqslant Ra_{F}\leqslant 1.8\times 10^{11}$ and cylindrical cells in the range $1.4\times 10^{10}\leqslant Ra_{F}\leqslant 1.2\times 10^{12}$ 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 fluctuations 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 in the bulk is essentially invariant with respect to both the 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 an 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 velocity.

We report an experimental study of confinement effects in quasi-2-D turbulent Rayleigh–Bénard convection. The experiments were conducted in five rectangular cells with their height $H$ and length $L$ being the same and fixed, while the width $W$ was different for each cell to produce lateral aspect ratios (${\it\Gamma}=W/H$) of 0.6, 0.3, 0.2, 0.15 and 0.1. Direct flow field measurements reveal that the large-scale flow slows down as ${\it\Gamma}$ decreases and there are more plumes travelling through the bulk region. Moreover, the reversal frequency of the large-scale flow is found to increase drastically in smaller ${\it\Gamma}$ cells, by more than 1000-fold for the highest value of Rayleigh number reached in the experiment. The reversal frequency can be well described by a stochastic model developed by Ni et al. (J. Fluid Mech., vol. 778, 2015, R5) and the probability density functions (PDF) of the time interval between successive reversals are found to follow Poisson statistics as in the 3-D system. It is further observed that the bulk temperature fluctuation increases significantly and its PDF changes from exponential to Gaussian as ${\it\Gamma}$ decreases. The influences of geometric confinement on the global heat transport are also investigated. The measured Nu–Ra relationship suggests that, as the lateral aspect ratio decreases, the relative weight of the boundary layer contribution in the global heat transport increases compared to that from the bulk. These results demonstrate that in the quasi-2-D geometry, geometric confinement has strong effects on both the global and local properties in turbulent convective flows, which are very different from the previous findings in 3-D and true 2-D systems.

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 enhancement of coherent heat fluxes and suppression of incoherent heat fluxes. The enhanced heat transport is associated with the increased coherency of thermal plumes, as a result of the suppression of small-scale turbulent fluctuations by polymers. The incoherent heat flux, arising from turbulent background fluctuations, makes no net contribution to heat transport. 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 significant modification of the plume coherent properties and enhancement of the local heat flux can be observed. Estimation of the plume emission rate suggests a stabilization of the thermal boundary layer by polymer additives.

We report an experimental study of the large-scale circulation (LSC) reversal in quasi-2D turbulent thermal convection, in which the aspect ratio ${\it\Gamma}$ ($=\text{height}/\text{length}$ of a rectangular box) is used as a parameter to perturb the stability of the LSC. It is found that the mean time interval $\langle {\it\tau}\rangle$ between two successive reversals increases strongly with increasing ${\it\Gamma}$. A stochastic model is proposed to incorporate the effect of the corner rolls. In the model, the aspect ratio serves as a tuning parameter for the relative weight of the corner rolls that damp the LSC. The model predictions for the shape of the bistable states of the system and $\langle {\it\tau}\rangle$ agree excellently with the experimental results, with $\langle {\it\tau}\rangle$ having an unexpected stretched exponential Rayleigh number dependence, ${\sim}\!\exp (Ra^{{\it\alpha}})$. We further show quantitatively that the main damping force of the LSC in a quasi-2D system is from the corner rolls rather than the viscous drag from the sidewalls, which bridges the difference found in quasi-2D and 3D systems.

We report the first experimental study of Lagrangian acceleration in turbulent Rayleigh–Bénard convection, using particle tracking velocimetry. A method has been developed to quantitatively evaluate and eliminate the uncertainties induced by temperature and refraction index fluctuations caused by the thermal plumes. It is found that the acceleration p.d.f. exhibits a stretched exponential form and that the probability for large magnitude of acceleration in the lateral direction is higher than those in the vertical directions, which can be attributed to the vortical motion of the thermal plumes. The local acceleration variance was obtained for various values of the three control parameters: the Rayleigh number (), the Prandtl number ( and 6.1) and the system size . These were then compared with the theoretically predicted dependence on these parameters for buoyancy-dominated turbulent flows and for homogeneous and isotropic turbulence, respectively. It is found that in the central region is dominated by contributions from the turbulent background rather than from the buoyancy force, and the Heisenberg–Yaglom relation holds in this region. From this, we obtain the first experimental results of the constant of the acceleration variance in the micro-scale Reynolds number range , which fills a gap in this constant in the lower end from the experimental side, and provides possible constraints for its high behaviour if a certain fitting function is attempted. In addition, acceleration correlation functions were obtained for different . It is found that the zero crossing time of acceleration correlation functions is at ( is the Kolmogorov time scale) over the range of spanned in our experiments, which is the same as the simulation results in isotropic turbulence, and the exponential decay time , which is larger than found experimentally for other types of turbulent flows with larger .