We report on the presence of the boundary zonal flow in rotating Rayleigh–Bénard convection evidenced by two-dimensional particle image velocimetry. Experiments were conducted in a cylindrical cell of aspect ratio $\varGamma =D/H=1$ between its diameter ($D$) and height ($H$). As the working fluid, we used various mixtures of water and glycerol, leading to Prandtl numbers in the range $6.6 \lesssim \textit {Pr} \lesssim 76$. The horizontal velocity components were measured at a horizontal cross-section at half height. The Rayleigh numbers were in the range $10^8 \leq \textit {Ra} \leq 3\times 10^9$. The effect of rotation is quantified by the Ekman number, which was in the range $1.5\times 10^{-5}\leq \textit {Ek} \leq 1.2\times 10^{-3}$ in our experiment. With our results we show the first direct measurements of the boundary zonal flow (BZF) that develops near the sidewall and was discovered recently in numerical simulations as well as in sparse and localized temperature measurements. We analyse the thickness $\delta _0$ of the BZF as well as its maximal velocity as a function of Pr, Ra and Ek, and compare these results with previous results from direct numerical simulations.

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.

For the Rayleigh-number range 107 ≲ Ra ≲ 1011 we report measurements of the Nusselt number Nu and of properties of the large-scale circulation (LSC) for cylindrical samples of helium gas (Prandtl number Pr = 0.674) that have aspect ratio Γ ≡ D/L = 0.50 (D and L are the diameter and the height respectively) and are heated from below. The results for Nu are consistent with recent direct numerical simulations. We measured the amplitude δ of the azimuthal temperature variation induced by the LSC at the sidewall, and the LSC circulation-plane orientation θ0, at three vertical positions. For the entire Ra range the LSC involves a convection roll that is coherent over the height of the system. However, this structure frequently collapses completely at irregular time intervals and then reorganizes from the incoherent flow. At small δ the probability distribution p(δ) increases linearly from zero; for Γ = 1 and Pr = 4.38 this increase is exponential. No evidence of a two-roll structure, with one above the other, was observed. This differs from recent direct numerical simulations for Γ = 0.5 and Pr = 0.7, where a one-roll LSC was found to exist only for Ra ≲ 109 to 1010, and from measurements for Γ = 0.5 and Pr ≃ 5, where one- and two-roll structures were observed with transitions between them at random time intervals.

Measurements over the Rayleigh-number range 108 ≲ R ≲ 1011 and Prandtl-number range 4.4≲σ≲29 that determine the torsional nature and amplitude of the oscillatory mode of the large-scale circulation (LSC) of turbulent Rayleigh–Bénard convection are presented. For cylindrical samples of aspect ratio Γ=1 the mode consists of an azimuthal twist of the near-vertical LSC circulation plane, with the top and bottom halves of the plane oscillating out of phase by half a cycle. The data for Γ=1 and σ=4.4 showed that the oscillation amplitude varied irregularly in time, yielding a Gaussian probability distribution centred at zero for the displacement angle. This result can be described well by the equation of motion of a stochastically driven damped harmonic oscillator. It suggests that the existence of the oscillations is a consequence of the stochastic driving by the small-scale turbulent background fluctuations of the system, rather than a consequence of a Hopf bifurcation of the deterministic system. The power spectrum of the LSC orientation had a peak at finite frequency with a quality factor Q≃5, nearly independent of R. For samples with Γ≥2 we did not find this mode, but there remained a characteristic periodic signal that was detectable in the area density ρp of the plumes above the bottom-plate centre. Measurements of ρp revealed a strong dependence on the Rayleigh number R, and on the aspect ratio Γ that could be represented by ρp ~ Γ2.7±0.3. Movies are available with the online version of the paper.

Non-Oberbeck–Boussinesq (NOB) effects on the Nusselt number $Nu$ and Reynolds number $\hbox{\it Re}$ in strongly turbulent Rayleigh–Bénard (RB) convection in liquids were investigated both experimentally and theoretically. In the experiments the heat current, the temperature difference, and the temperature at the horizontal midplane were measured. Three cells of different heights $L$, all filled with water and all with aspect ratio $\Gamma$ close to 1, were used. For each $L$, about 1.5 decades in $Ra$ were covered, together spanning the range $10^8 \,{\le}\, Ra \,{\le}\, 10^{11}$. For the largest temperature difference between the bottom and top plates, $\Delta \,{=}\, 40$K, the kinematic viscosity and the thermal expansion coefficient, owing to their temperature dependence, varied by more than a factor of 2. The Oberbeck–Boussinesq (OB) approximation of temperature-independent material parameters thus was no longer valid. The ratio $\chi$ of the temperature drops across the bottom and top thermal boundary layers became as small as $\chi\,{=}\,0.83$, which may be compared with the ratio $\chi \,{=}\, 1$ in the OB case. Nevertheless, the Nusselt number $Nu$ was found to be only slightly smaller (by at most 1.4%) than in the next larger cell with the same Rayleigh number, where the material parameters were still nearly height independent. The Reynolds numbers in the OB and NOB case agreed with each other within the experimental resolution of about 2%, showing that NOB effects for this parameter were small as well. Thus $Nu$ and $\hbox{\it Re}$ are rather insensitive against even significant deviations from OB conditions. Theoretically, we first account for the robustness of $Nu$ with respect to NOB corrections: the NOB effects in the top boundary layer cancel those which arise in the bottom boundary layer as long as they are linear in the temperature difference $\Delta$. The net effects on $Nu$ are proportional to $ \Delta^2$ and thus increase only slowly and still remain minor despite drastic material-parameter changes. We then extend the Prandtl–Blasius boundary-layer theory to NOB Rayleigh–Bénard flow with temperature-dependent viscosity and thermal diffusivity. This allows calculation of the shift in the bulk temperature, the temperature drops across the boundary layers, and the ratio $\chi$ without the introduction of any fitting parameter. The calculated quantities are in very good agreement with experiment. When in addition we use the experimental finding that for water the sum of the top and bottom thermal boundary-layer widths (based on the slopes of the temperature profiles at the plates) remains unchanged under NOB effects within the experimental resolution, the theory also gives the measured small Nusselt-number reduction for the NOB case. In addition, it predicts an increase by about 0.5% of the Reynolds number, which is also consistent with the experimental data. By studying theoretically hypothetical liquids for which only one of the material parameters is temperature dependent, we are able to shed further light on the origin of NOB corrections in water: while the NOB deviation of $\chi$ from its OB value $\chi \,{=}\, 1$ mainly originates from the temperature dependence of the viscosity, the NOB correction of the Nusselt number primarily originates from the temperature dependence of the thermal diffusivity. Finally, we give predictions from our theory for the NOB corrections if glycerol were used as the operating liquid.

The dynamics of a single bubble rising in a viscous Newtonian fluid was investigated both experimentally by a particle image velocimetry (PIV) device and numerically using the free-energy-based lattice Boltzmann (LB) model. The rise velocity, bubble shape and flow field were considered for various bubble volumes in axisymmetric flow conditions. Experimentally, the flow measurements by the PIV device revealed the wake increasing with the bubble volume. Such an evolution is linked to the deformation of bubble shape from spherical for small bubbles to flattened at the bottom for large bubbles. The LB simulations compare satisfactorily with our experimental data for both the bubble shape and drag coefficient over the range of Reynolds number ($ 0.033 \leq Re \leq 1.8 $). With a more extended flow structure around the bubble compared to experiments, the two-dimensional approach shows some limitations in its quantitative description. Fully three-dimensional simulations are necessary, especially for bigger bubbles with $ Re > 1.8 $.

We present high-precision measurements of the Nusselt number $\cal{N}$ as a function of the Rayleigh number $R$ for cylindrical samples of water (Prandtl number $\sigma \,{=}\, 4.38$) with diameters $D \,{=}\, 49.7, 24.8,$ and 9.2cm, all with aspect ratio $\Gamma \,{\equiv}\, D/L \,{\simeq}\,1$ ($L$ is the sample height). In addition, we present data for $D \,{=}\, 49.7$ and $\Gamma \,{=}\, 1.5, 2, 3,$ and 6. For each sample the data cover a range of a little over a decade of $R$. For $\Gamma \,{\simeq}\,1$ they jointly span the range $10^7 \lesssim R \lesssim 10^{11}$. Where needed, the data were corrected for the influence of the finite conductivity of the top and bottom plates and of the sidewalls on the heat transport in the fluid to obtain estimates of $\cal{N}_{\infty}$ for plates with infinite conductivity and sidewalls of zero conductivity. For $\Gamma \,{\simeq}\,1$ the effective exponent $\gamma_{\hbox{\scriptsize\it eff}}$ of ${\cal N}_{\infty} \,{=}\, N_0 R^{\gamma_{\hbox{\scriptsize\it eff}}}$ ranges from 0.28 near $R \,{=}\, 10^8$ to 0.333 near $R \,{\simeq}\,7\,{\times}\,10^{10}$. For $R \lesssim 10^{10}$ the results are consistent with the Grossmann–Lohse model. For larger $R$, where the data indicate that ${\cal N}_\infty(R) \,{\sim}\, R^{1/3}$, the theory has a smaller $\gamma_{\hbox{\scriptsize\it eff}}$ than $1/3$ and falls below the data. The data for $\Gamma \,{>}\, 1$ are only a few percent smaller than the $\Gamma \,{=}\, 1$ results.

We present high-precision measurements of the Nusselt number $\cal N$ as a function of the Rayleigh number $R$ for cylindrical samples of water (Prandtl number $\sigma \,{=}\, 4.4$) with a diameter $D$ of 49.7 cm and heights $L \,{=}\, 116.3, 74.6$, and 50.6 cm, as well as for $D \,{=}\, 24.8$ cm and $L \,{=}\, 90.2$ cm. For each aspect ratio $\Gamma \,{\equiv}\, D/L \,{=}\, 0.28, 0.43, 0.67$, and 0.98 the data cover a range of a little over a decade of $R$. The maximum $R \,{\simeq}\, 10^{12}$ and Nusselt number ${\cal N} \,{\simeq}\, 600$ were reached for $\Gamma \,{=}\, 0.43$ and $D \,{=}\, 49.7$. The data were corrected for the influence of the finite conductivity of the top and bottom plates on the heat transport in the fluid to obtain estimates of $\cal N_{\infty}$ for plates with infinite conductivity. The results for ${\cal N}_{\infty}$ and $\Gamma \,{\geq}\, 0.43$ are nearly independent of $\Gamma$. For $\Gamma \,{=}\, 0.275$${\cal N}_{\infty}$ falls about 2.5% below the other data. For $R \,{\lesssim}\,10^{11}$, the effective exponent $\gamma_{\hbox{\scriptsize\it eff}}$ of ${\cal N}_{\infty} \,{=}\, N_0 R^{\gamma_{\hbox{\scriptsize\it eff}}}$ is about 0.32, larger than those of the Grossmann–Lohse model with its current parameters by about 0.01. For the largest Rayleigh numbers covered for $\Gamma \,{=}\, $0.98, 0.67, and 0.43, $\gamma_{\hbox{\scriptsize\it eff}}$ saturates at the asymptotic value $\gamma \,{=}\, 1/3$ of the Grossmann–Lohse model. The data do not reveal any crossover to a Kraichnan regime with $\gamma_{\hbox{\scriptsize\it eff}} \,{>}\, 1/3$.