Recent experiments and simulations have sparked growing interest in the study of Rayleigh–Bénard convection in very slender cells. One pivotal inquiry arising from this interest is the elucidation of the flow structure within these very slender cells. Here we employ tomographic particle image velocimetry, for the first time, to capture experimentally the full-field three-dimensional and three-component velocity field in a very slender cylindrical cell with aspect ratio $\Gamma =1/10$. The experiments cover a Rayleigh number range $5.0 \times 10^8 \leqslant Ra \leqslant 5.0 \times 10^9$ and Prandtl number 5.7. Our experiments reveal that the flow structure in the $\Gamma =1/10$ cell is neither in the multiple-roll form nor in the simple helical form; instead, the ascending and descending flows can intersect and cross each other, resulting in the crossing events. These crossing events separate the flow into segments; within each segment, the ascending and descending flows ascend or descend side by side vertically or in the twisting manner, and the twisting is not unidirectional, while the segments near the boundary can also be in the form of a donut like structure. By applying the mode decomposition analyses to the measured three-dimensional velocity fields, we identified the crossing events as well as the twisting events for each instantaneous flow field. Statistical analysis of the modes reveals that as $Ra$ increases, the average length of the segments becomes smaller, and the average number of segments increases from 2.5 to 3.9 in the $Ra$ range of our experiments.

We studied flow organization and heat transfer properties in mixed turbulent convection within Poiseuille–Rayleigh–Bénard channels subjected to temporally modulated sinusoidal wall temperatures. Three-dimensional direct numerical simulations were performed for Rayleigh numbers in the range $10^6 \leqslant Ra \leqslant 10^8$, a Prandtl number $Pr = 0.71$ and a bulk Reynolds number $Re_b \approx 5623$. We found that high-frequency wall temperature oscillations had minimal impact on flow structures, while low-frequency oscillations induced adaptive changes, forming stable stratified layers during cooling. Proper orthogonal decomposition (POD) analysis revealed a dominant streamwise unidirectional shear flow mode. Large-scale rolls oriented in the streamwise direction appeared as higher POD modes and were significantly influenced by lower-frequency wall temperature variations. Long-time-averaged statistics showed that the Nusselt number increased with decreasing frequency by up to 96 %, while the friction coefficient varied by less than 15 %. High-frequency modulation predominantly influenced near-wall regions, enhancing convective effects, whereas low frequencies reduced these effects via stable stratified layer formation. Phase-averaged statistics showed that high-frequency modulation resulted in phase-stable streamwise velocity and temperature profiles, while low-frequency modulation caused significant variations due to weakened turbulence. Turbulent kinetic energy (TKE) profiles remained high near the wall during both heating and cooling at high frequency, but decreased during cooling at low frequencies. A TKE budget analysis revealed that during heating, TKE production was dominated by shear near the wall and by buoyancy in the bulk region; while during cooling, the production, distribution and dissipation of TKE were all nearly zero.

We present an experimental study on the drag reduction by polymers in Taylor–Couette turbulence at Reynolds numbers ($Re$) ranging from $4\times 10^3$ to $2.5\times 10^4$. In this $Re$ regime, the Taylor vortex is present and accounts for more than 50 % of the total angular velocity flux. Polyacrylamide polymers with two different average molecular weights are used. It is found that the drag reduction rate increases with polymer concentration and approaches the maximum drag reduction (MDR) limit. At MDR, the friction factor follows the $-0.58$ scaling, i.e. $C_f \sim Re^{-0.58}$, similar to channel/pipe flows. However, the drag reduction rate is about $20\,\%$ at MDR, which is much lower than that in channel/pipe flows at comparable $Re$. We also find that the Reynolds shear stress does not vanish and the slope of the mean azimuthal velocity profile in the logarithmic layer remains unchanged at MDR. These behaviours are reminiscent of the low drag reduction regime reported in channel flow (Warholic et al., Exp. Fluids, vol. 27, no. 5, 1999, pp. 461–472). We reveal that the lower drag reduction rate originates from the fact that polymers strongly suppress the turbulent flow while only slightly weaken the mean Taylor vortex. We further show that polymers steady the velocity boundary layer and suppress the small-scale Görtler vortices in the near-wall region. The former effect reduces the emission rate of both intense fast and slow plumes detached from the boundary layer, resulting in less flux transport from the inner cylinder to the outer one and reduces energy input into the bulk turbulent flow. Our results suggest that in turbulent flows, where secondary flow structures are statistically persistent and dominate the global transport properties of the system, the drag reduction efficiency of polymer additives is significantly diminished.

We studied the transport and deposition behaviour of point particles in Rayleigh–Bénard convection cells subjected to Couette-type wall shear. Direct numerical simulations (DNSs) are performed for Rayleigh number ($Ra$) in the range $10^{7} \leq Ra \leq ~10^9$ with a fixed Prandtl number $Pr = 0.71$, while the wall-shear Reynolds number ($Re_w$) is in the range $0 \leq Re_w \leq ~12\,000$. With the increase of $Re_w$, the large-scale rolls expanded horizontally, evolving into zonal flow in two-dimensional simulations or streamwise-oriented rolls in three-dimensional simulations. We observed that, for particles with a small Stokes number ($St$), they either circulated within the large-scale rolls when buoyancy dominated or drifted near the walls when shear dominated. For medium $St$ particles, pronounced spatial inhomogeneity and preferential concentration were observed regardless of the prevailing flow state. For large $St$ particles, the turbulent flow structure had a minor influence on the particles’ motion; although clustering still occurred, wall shear had a negligible influence compared with that for medium $St$ particles. We then presented the settling curves to quantify the particle deposition ratio on the walls. Our DNS results aligned well with previous theoretical predictions, which state that small $St$ particles settle with an exponential deposition ratio and large $St$ particles settle with a linear deposition ratio. For medium $St$ particles, where complex particle–turbulence interaction emerges, we developed a new model describing the settling process with an initial linear stage followed by a nonlinear stage. Unknown parameters in our model can be determined either by fitting the settling curves or using empirical relations. Compared with DNS results, our model also accurately predicts the average residence time across a wide range of $St$ for various $Re_w$.

To date, a comprehensive understanding of the influence of the Prandtl number ($Pr$) on flow topology in turbulent Rayleigh–Bénard convection (RBC) remains elusive. In this study, we present an experimental investigation into the evolution of flow topology in quasi-two-dimensional turbulent RBC with $7.0 \leq Pr \leq 244.2$ and $2.03\times 10^{8} \leq Ra \leq 2.81\times 10^{9}$. Particle image velocimetry (PIV) measurements reveal the flow transitions from multiple-roll state to single-roll state with increasing $Ra$, and the transition is hindered with increasing $Pr$, i.e. the transitional Rayleigh number $Ra_t$ increases with $Pr$. We mapped out a phase diagram on the flow topology change on $Ra$ and $Pr$, and identified the scaling of $Ra_t$ on $Pr$: $Ra_t \sim Pr^{0.93}$ in the low $Pr$ range, and $Ra_t \sim Pr^{3.3}$ in the high $Pr$ range. The scaling in the low $Pr$ range is consistent with the model of balance of energy dissipation time and plume travel time that we proposed in our previous study, while the scaling in the high $Pr$ range implies a new governing mechanism. For the first time, the scaling of $Re$ on $Ra$ and $Pr$ is acquired through full-field PIV velocity measurement, $Re \sim Ra^{0.63}\,Pr^{-0.87}$. We also propose that increasing horizontal velocity promotes the formation of the large-scale circulation (LSC), especially for the high $Pr$ case. Our proposal was verified by achieving LSC through introducing horizontal driving force $Ra_H$ by tilting the convection cell with a small angle.

We report an experimental study about the effect of an obstructed centre on heat transport and flow reversal by inserting an adiabatic cylinder at the centre of a quasi-two-dimensional Rayleigh–Bénard convection cell. The experiments are carried out in a Rayleigh number ($Ra$) range of $2\times 10^7 \leq Ra \leq 2\times 10^9$ and at a Prandtl number ($Pr$) of $5.7$. It is found that for low $Ra$, the obstructed centre leads to a heat transfer enhancement of up to 21 $\%$, while as $Ra$ increases, the magnitude of the heat transfer enhancement decreases and the heat transfer efficiency ($Nu$) eventually converges to that of the unobstructed normal cell. Particle image velocimetry measurements show that the heat transfer enhancement originates from the change in flow topology due to the presence of the cylindrical obstruction. In the low-$Ra$ regime the presence of the obstruction promotes the transition of the flow topology from the four-roll state to the abnormal single-roll state then to the normal single-roll state with increasing obstruction size. While in the high-$Ra$ regime, the flow is always in the single-roll state regardless of the obstruction size, although the flow becomes more coherent with the size of the obstruction. We also found that in the presence of the cylindrical obstruction, the stability of the corner vortices is significantly reduced, leading to a large reduction in the frequency of flow reversals.

We studied the flow organization and heat transfer properties in two-dimensional and three-dimensional Rayleigh–Bénard cells that are imposed with different types of wall shear. The external wall shear is added with the motivation of manipulating flow mode to control heat transfer efficiency. We imposed three types of wall shear that may facilitate the single-roll, the horizontally stacked double-roll, and the vertically stacked double-roll flow modes, respectively. Direct numerical simulations are performed for fixed Rayleigh number $Ra = 10^{8}$ and fixed Prandtl number $Pr = 5.3$, while the wall-shear Reynolds number ($Re_{w}$) is in the range $60 \leqslant Re_{w} \leqslant 6000$. Generally, we found enhanced heat transfer efficiency and global flow strength with the increase of $Re_{w}$. However, even with the same magnitude of global flow strength, the heat transfer efficiency varies significantly when the cells are under different types of wall shear. An interesting finding is that by increasing the wall-shear strength, the thermal turbulence is relaminarized, and more surprisingly, the heat transfer efficiency in the laminar state is higher than that in the turbulent state. We found that the enhanced heat transfer efficiency at the laminar regime is due to the formation of more stable and stronger convection channels. We propose that the origin of thermal turbulence laminarization is the reduced amount of thermal plumes. Because plumes are mainly responsible for turbulent kinetic energy production, when the detached plumes are swept away by the wall shear, the reduced number of plumes leads to weaker turbulent kinetic energy production. We also quantify the efficiency of facilitating heat transport via external shearing, and find that for larger $Re_{w}$, the enhanced heat transfer efficiency comes at a price of a larger expenditure of mechanical energy.

We present an experimental study of the large-scale vortex (or large-scale circulation, LSC) in turbulent Rayleigh–Bénard convection in a $\varGamma =\text {diameter}/\text {height}=2$ cylindrical cell. The working fluid is deionized water with Prandtl number ($Pr$) around 5.7, and the Rayleigh number ($Ra$) ranges from $7.64\times 10^7$ to $6.06\times 10^8$. We measured the velocity field in various vertical cross-sectional planes by using the planar particle image velocimetry technique. The velocity measurement in the LSC central plane shows that the flow is in the single-roll form, and the centre of the single-roll (vortex) does not always stay at the centre of the cell; instead, it orbits periodically in the direction opposite to the flow direction of the LSC, with its trajectory in the shape of an ellipse. The velocity measurements in the three vertical planes in parallel to the LSC central plane indicate that the flow is in the vortex tube form horizontally filling almost the whole cell, and the centre line of the vortex tube is consistent with the so-called ‘jump rope’ form proposed by a previous study that combined numerical simulation and local velocity measurements in the low $Pr$ case (Vogt et al., Proc. Natl Acad. Sci. USA, vol. 115, 2018, pp. 12674–12679). In addition, we found that the oscillation of the local velocity in $\varGamma =2$ cells originates from the periodical orbiting of the vortex centre. Our velocity measurements further indicate that the vortex centre orbiting is absent in $\varGamma =1$ cells, at least in the $Ra$ range of our experiments.

In this paper, we designed two different configurations with locally isothermal sidewalls, where the temperature is set to be the bulk temperature, to control the large-scale circulation in turbulent Rayleigh–Bénard convection, namely two-point control and four-point control. At fixed Rayleigh number $Ra=10^8$ and Prandtl number $Pr=2$, a series of direct numerical simulations are performed on both two-dimensional (2-D) and quasi-two-dimensional (quasi-2-D) cavities with both types of control, where the width of the control area is fixed at $\delta _c=0.05$ and the vertical distance from the cavity centre $h_c$ varies from 0 to 0.45 with an interval of 0.05. Our results show that the control effect depends on $h_c$, the control configurations as well as the flow dimensions. For 2-D cavities, both two-point control and four-point control suppress the flow reversal when $h_c \geq 0.05$, accompanied by the enhancement of vertical heat transfer and the strength of the large-scale circulation. For quasi-2-D cavities, the suppression of the flow reversals is obvious with two-point control and $h_c\geq 0.05$, while the effect is rather limited with four-point control. Further experiments with $Pr=5.7$ and $Ra$ up to $7.36\times10^8$ show that two-point control with $h_c=0.15$ can effectively suppress the flow reversal, while two-point control with $h_c=0$ can suppress the reversals at low $Ra=1.93\times 10^8$ and activate them at higher $Ra=7.36\times 10^8$, which agrees well with our numerical simulations.

We present a numerical study of the flow states and reversals of the large-scale circulation (LSC) in a two-dimensional circular Rayleigh–Bénard cell. Long-time direct numerical simulations are carried out in the Rayleigh number ($Ra$) range $10^{7} \leqslant Ra \leqslant 10^{8}$ and Prandtl number ($Pr$) range $2.0 \leqslant Pr \leqslant 20.0$. We found that a new, long-lived, chaotic flow state exists, in addition to the commonly observed circulation states (the LSC in the clockwise and counterclockwise directions). The circulation states consist of one primary roll in the middle and two secondary rolls near the top and bottom circular walls. The primary roll becomes stronger and larger, while the two secondary rolls diminish, with increasing $Ra$. Our results suggest that the reversal of the LSC is accompanied by the secondary rolls growing, breaking the primary roll and then connecting to form a new primary roll with reversed direction. We mapped out the phase diagram of the existence of the LSC and the reversal in the $Ra\text{--}Pr$ space, which reveals that the flow is in the circulation states when $Ra$ is large and $Pr$ is small. The reversal of the LSC can only occur in a limited $Pr$ range. The phase diagram can be understood in terms of competition between the thermal and viscous diffusions. We also found that the internal flow states manifested themselves into global properties such as Nusselt and Reynolds numbers.

We present an experimental study on controlling the number of vortices and the torque in a Taylor–Couette flow of water for Reynolds numbers from 660 to 1320. Different flow states are achieved in the annulus of width $d$ between the inner rotating and outer stationary cylinders through manipulating the initial height of the water annulus. We show that the torque exerted on the inner cylinder of the Taylor–Couette system can be reduced by up to 20 % by controlling the flow at a state where fewer than the nominal number of vortices develop between the cylinders. This flow state is achieved by starting the system with an initial water annulus height $h_0$ (which nominally corresponds to $h_0/d$ vortices), then gradually adding water into the annulus while the inner cylinder keeps rotating. During this filling process the flow topology is so persistent that the number of vortices does not increase; instead, the vortices are greatly stretched in the axial (vertical) direction. We show that this state with stretched vortices is sustainable until the vortices are stretched to around 2.05 times their nominal size. Our experiments reveal that by manipulating the initial height of the liquid annulus we are able to generate different flow states and demonstrate how the different flow states manifest themselves in global momentum transport.

We report a comparative experimental study of the reversal of the large-scale circulation in turbulent Rayleigh–Bénard convection in a quasi-two-dimensional corner-less cell where the corner vortices are absent and in a quasi-two-dimensional normal cell where the corner vortices are present. It is found that in the corner-less cell the reversal frequency exhibits a slow decrease followed by a fast decrease with increasing Rayleigh number $Ra$, separated by a transitional $Ra$ ($Ra_{t,r}$). The transition is similar to that in the normal cell, and $Ra_{t,r}$ is almost the same for both cells. Despite the similarities, the reversal frequency is greatly reduced in the corner-less cell. The reduction of the reversal frequency is more significant, in terms of both the amplitude and the scaling exponent, in the high-$Ra$ regime. In addition, we classified the reversals into main-vortex-led and corner-vortex-led, and found that both types exist in the normal cell while only the former exists in the corner-less cell. The frequency of main-vortex-led reversal in the normal cell is found to be in excellent agreement with the frequency of reversals in the corner-less cell. Our results reveal for the first time the quantitative role of the corner vortices in the occurrence of the reversals of the large-scale circulation.

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.

We present experimental studies of higher-order modes of the flow in turbulent thermal convection in cells of aspect ratio ($\unicode[STIX]{x1D6E4}$) 1 and 0.5. The working fluid is water with the Prandtl number ($Pr$) kept at around 5.0. The Rayleigh number ($Ra$) ranges from $9\times 10^{8}$ to $6\times 10^{9}$ for $\unicode[STIX]{x1D6E4}=1$ and from $1.6\times 10^{10}$ to $7.2\times 10^{10}$ for $\unicode[STIX]{x1D6E4}=0.5$. We found that in $\unicode[STIX]{x1D6E4}=1$ cells, the first mode, which corresponds to the large-scale circulation (LSC), dominates the flow. The second mode (quadrupole mode), the third mode (sextupole mode) and the fourth mode (octupole mode) are very weak, on average these higher-order modes each contains less than 4 % of the total flow energy. In $\unicode[STIX]{x1D6E4}=0.5$ cells, the first mode is still the strongest but less dominant, the second mode becomes stronger which contains 13.7 % of the total flow energy and the third and the fourth modes are also stronger (containing 6.5 % and 1.1 % of the total flow energy respectively). It is found that during a reversal/cessation, the amplitude of the second mode and the remaining modes experiences a rapid increase followed by a decrease, which is opposite to the behaviour of the amplitude of the first mode – it decreases to almost zero then rebounds. In addition, it is found that during the cessation (reversal) of the LSC, the second mode dominates, containing 51.3 % (50.1 %) of the total flow energy, which reveals that the commonly called cessation event is not the cessation of the entire flow but only the cessation of the first mode (LSC). The experiment reveals that the second mode and the remaining higher-order modes play important roles in the dynamical process of the reversal/cessation of the LSC. We also show direct evidence that the first mode is more efficient for heat transfer. Furthermore, our study reveals that, during the cessation/reversal of the LSC, $Nu$ drops to its local minimum and the minimum of $Nu$ is ahead of the minimum of the amplitude of the LSC; and reversals can be distinguished from cessations in terms of global heat transport. A direct velocity measurement reveals the flow structure of the first- and higher-order modes.

We report an experimental study of the large-scale circulation (LSC) in a turbulent Rayleigh–Bénard convection cell with aspect ratio unity. The temperature-extrema-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 based on these two angles: the azimuthal mode and the translational or sloshing mode that is perpendicular to the vertical circulation plane of the LSC. Comparing to the previous sinusoidal-fitting (SF) method, it is found that both the TEE and the SF methods give the same information about the azimuthal motion of the LSC, but the TEE method in addition can provide information about the sloshing motion of the LSC. The sloshing motion is found to oscillate time-periodically around the cell's central vertical axis with an amplitude being nearly independent of the turbulent intensity and to have a π/2 phase difference with the torsional mode. It is further found that the azimuthal angular positions of the hot ascending and cold descending flows oscillate out of phase with each other by π, which leads to the observations of the torsional mode when these two flows are near the top and the bottom plates, respectively, and of the sloshing mode when they are both near the mid-height plane. A direct velocity measurement further confirms the existence of the bulk sloshing mode of the flow field.

We report an experimental study on the onset of the large-scale coherent mean flow in Rayleigh–Bénard turbulent convection. Shadowgraph and particle image velocimetry techniques are used to visualize the motion of thermal plumes and measure the velocity of the plumes and of the ‘background’ flow field, as the fluid motion evolves from quiescent to steady state. The experiment reveals the dynamical origin of the initial horizontal motion required by the large-scale flow: the fluid entrainment caused by the plume's vertical motion generates vortices surrounding the plume itself. These vortices in turn generate the initial horizontal motion of the flow field. Two types of interactions have been identified: (i) direct plume–vortex interaction; and (ii) plume–plume interaction via vortices. These interactions and the interaction and merging of the vortices from neighbouring plumes lead to groupings and/or merging of plumes, which in turn generate vortices of even larger scale. As a result of these interactions, the convective flow evolves into a coherent rotatory motion consisting of mainly the plumes themselves and spanning the whole convection box. This study clearly demonstrates that it is the thermal plumes that initiate the horizontal large-scale flow across the top and bottom conducting plates.