Heat transport in turbulent Rayleigh-Benard convection: Effect of finite top- and bottom-plate conductivity

We describe three apparatus, known as the large, medium, and small apparatus, used for high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of fluid and present results illustrating the influence of the finite conductivity of the top and bottom plates on the heat transport in the fluid. We used water samples at a mean temperature of 40 degrees C (Prandtl number sigma = 4.4). The samples in the large apparatus had a diameter D of 49.69 cm and heights L = 116.33, 74.42, 50.61, and 16.52 cm. For the medium apparatus we had D = 24.81 cm, and L = 90.20 and 24.76 cm. The small apparatus contained a sample with D = 9.21 cm, and L = 9.52 cm. For each aspect ratio Gamma = D/L the data covered a range of a little over a decade of R. The maximum R = 10^12 with Nusselt numbers N = 600 was reached for Gamma = 0.43. Measurements were made with both Aluminum and Copper top and bottom plates of nominally identical size and shape. For the large and medium apparatus the results with Aluminum plates fall below those obtained with Copper plates, thus confirming qualitatively the prediction by Verzicco that plates of finite conductivity diminish the heat transport in the fluid. The Nusselt number N_infinity for plates with infinite conductivity was estimated by fitting simultaneously Aluminum- and Copper-plate data sets to an effective powerlaw for N_infinity multiplied by a correction factor f(X) = 1 - exp[-(aX)^b] that depends on the ratio X of the thermal resistance of the fluid to that of the plates as suggested by Verzicco. Within their uncertainties the parameters a and b were independent of Gamma for the large apparatus and showed a small Gamma-dependence for the medium apparatus. The correction was larger for the large, smaller for the medium, and negligible for the small apparatus.Comment: 35 pages, 11 figures. Under consideration for publication in Phys. of Fluid

Rayleigh-B\'{e}nard convection in a homeotropically aligned nematic liquid crystal

We report experimental results for convection near onset in a thin layer of a homeotropically aligned nematic liquid crystal heated from below as a function of the temperature difference $\Delta T$ and the applied vertical magnetic field $H$ and compare them with theoretical calculations. The experiments cover the field range 8 \alt h \equiv H/ H_{F} \alt 80 ($H_F =$ is the Fr\'eedericksz field). For $h$ less than a codimension-two field $h_{ct} \simeq 46$ the bifurcation is subcritical and oscillatory, with travelling- and standing-wave transients. Beyond $h_{ct}$ the bifurcation is stationary and subcritical until a tricritical field $h_t= 57.2$ is reached, beyond which it is supercritical. The bifurcation sequence as a function of $h$ found in the experiment confirms the qualitative aspects of the theoretical predictions. However, the value of $h_{ct}$ is about 10% higher than the predicted value and the results for $k_c$ are systematically below the theory by about 2% at small $h$ and by as much as 7% near $h_{ct}$. At $h_{ct}$, $k_c$ is continuous within the experimental resolution whereas the theory indicates a 7% discontinuity. The theoretical tricritical field $h_t^{th} = 51$ is somewhat below the experimental one. The fully developed flow above $R_c$ for $h < h_{ct}$ is chaotic. For $h_{ct} < h < h_t$ the subcritical stationary bifurcation also leads to a chaotic state. The chaotic states persist upon reducing the Rayleigh number below $R_c$, i.e. the bifurcation is hysteretic. Above the tricritical field $h_t$, we find a bifurcation to a time independent pattern which within our resolution is non-hysteretic.Comment: 15 pages incl. 23 eps figure

Heat transport by turbulent Rayleigh-B\'enard convection for $\Pra\ \simeq 0.8and and 3\times 10^{12} \alt \Ra\ \alt 10^{15}:Aspectratio: Aspect ratio \Gamma = 0.50$

We report experimental results for heat-transport measurements, in the form of the Nusselt number \Nu, by turbulent Rayleigh-B\'enard convection in a cylindrical sample of aspect ratio $\Gamma \equiv D/L = 0.50$ ($D = 1.12$ m is the diameter and $L = 2.24$ m the height). The measurements were made using sulfur hexafluoride at pressures up to 19 bars as the fluid. They are for the Rayleigh-number range 3\times 10^{12} \alt \Ra \alt 10^{15} and for Prandtl numbers \Pra\ between 0.79 and 0.86. For \Ra < \Ra^*_1 \simeq 1.4\times 10^{13} we find \Nu = N_0 \Ra^{\gamma_{eff}} with $\gamma_{eff} = 0.312 \pm 0.002$, consistent with classical turbulent Rayleigh-B\'enard convection in a system with laminar boundary layers below the top and above the bottom plate. For \Ra^*_1 < \Ra < \Ra^*_2 (with \Ra^*_2 \simeq 5\times 10^{14}) $\gamma_{eff}$ gradually increases up to $0.37\pm 0.01$. We argue that above \Ra^*_2 the system is in the ultimate state of convection where the boundary layers, both thermal and kinetic, are also turbulent. Several previous measurements for $\Gamma = 0.50$ are re-examined and compared with the present results.Comment: 44 pages, 18 figures, submitted to NJ

Heat transport by turbulent Rayleigh-B\'enard convection for $\Pra\ \simeq 0.8and and 4\times 10^{11} \alt \Ra\ \alt 2\times10^{14}:Ultimate−statetransitionforaspectratio: Ultimate-state transition for aspect ratio \Gamma = 1.00$

We report experimental results for heat-transport measurements by turbulent Rayleigh-B\'enard convection in a cylindrical sample of aspect ratio $\Gamma \equiv D/L = 1.00$ ($D = 1.12$ m is the diameter and $L = 1.12$ m the height). They are for the Rayleigh-number range 4\times10^{11} \alt \Ra \alt 2\times10^{14} and for Prandtl numbers \Pra\ between 0.79 and 0.86. For \Ra < \Ra^*_1 \simeq 2\times 10^{13} we find \Nu = N_0 \Ra^{\gamma_{eff}} with $\gamma_{eff} = 0.321 \pm 0.002$ and $N_0 = 0.0776$, consistent with classical turbulent Rayleigh-B\'enard convection in a system with laminar boundary layers below the top and above the bottom plate and with the prediction of Grossmann and Lohse. For \Ra > \Ra_1^* the data rise above the classical-state power-law and show greater scatter. In analogy to similar behavior observed for $\Gamma = 0.50$, we interpret this observation as the onset of the transition to the ultimate state. Within our resolution this onset occurs at nearly the same value of \Ra_1^* as it does for $\Gamma = 0.50$. This differs from an earlier estimate by Roche {\it et al.} which yielded a transition at \Ra_U \simeq 1.3\times 10^{11} \Gamma^{-2.5\pm 0.5}. A $\Gamma$-independent \Ra^*_1 would suggest that the boundary-layer shear transition is induced by fluctuations on a scale less than the sample dimensions rather than by a global $\Gamma$-dependent flow mode. Within the resolution of the measurements the heat transport above \Ra_1^* is equal for the two $\Gamma$ values, suggesting a universal aspect of the ultimate-state transition and properties. The enhanced scatter of \Nu\ in the transition region, which exceeds the experimental resolution, indicates an intrinsic irreproducibility of the state of the system.Comment: 17 pages, including 2 pages of data tables and 56 references. Submitted to New J. Phy

A model of diffusion in a potential well for the dynamics of the large-scale circulation in turbulent Rayleigh-Benard convection

Experimental measurements of properties of the large-scale circulation (LSC) in turbulent convection of a fluid heated from below in a cylindrical container of aspect ratio one are presented and used to test a model of diffusion in a potential well for the LSC. The model consists of a pair of stochastic ordinary differential equations motivated by the Navier-Stokes equations. The two coupled equations are for the azimuthal orientation theta_0, and for the azimuthal temperature amplitude delta at the horizontal midplane. The dynamics is due to the driving by Gaussian distributed white noise that is introduced to represent the action of the small-scale turbulent fluctuations on the large-scale flow. Measurements of the diffusivities that determine the noise intensities are reported. Two time scales predicted by the model are found to be within a factor of two or so of corresponding experimental measurements. A scaling relationship predicted by the model between delta and the Reynolds number is confirmed by measurements over a large experimental parameter range. The Gaussian peaks of probability distributions p(delta) and p(\dot\theta_0) are accurately described by the model; however the non-Gaussian tails of p(delta) are not. The frequency, angular change, and amplitude bahavior during cessations are accurately described by the model when the tails of the probability distribution of $\delta$ are used as experimental input.Comment: 17 pages, 17 figure

Interplay between the electrical transport properties of GeMn thin films and Ge substrates

We present evidence that electrical transport studies of epitaxial p-type GeMn thin films fabricated on high resistivity Ge substrates are severely influenced by parallel conduction through the substrate, related to the large intrinsic conductivity of Ge due to its small bandgap. Anomalous Hall measurements and large magneto resistance effects are completely understood by taking a dominating substrate contribution as well as the measurement geometry into account. It is shown that substrate conduction persists also for well conducting, degenerate, p-type thin films, giving rise to an effective two-layer conduction scheme. Using n-type Ge substrates, parallel conduction through the substrate can be reduced for the p-type epi-layers, as a consequence of the emerging pn-interface junction. GeMn thin films fabricated on these substrates exhibit a negligible magneto resistance effect. Our study underlines the importance of a thorough characterization and understanding of possible substrate contributions for electrical transport studies of GeMn thin films.Comment: 9 pages, 9 figure

Power-Law Behavior of Power Spectra in Low Prandtl Number Rayleigh-Benard Convection

The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Benard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power-law is found to arise from quasi-discontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics.Comment: (10 pages, 6 figures

Clustering in a precipitate free GeMn magnetic semiconductor

We present the first study relating structural parameters of precipitate free Ge0.95Mn0.05 films to magnetisation data. Nanometer sized clusters - areas with increased Mn content on substitutional lattice sites compared to the host matrix - are detected in transmission electron microscopy (TEM) analysis. The films show no overall spontaneous magnetisation at all down to 2K. The TEM and magnetisation results are interpreted in terms of an assembly of superparamagnetic moments developing in the dense distribution of clusters. Each cluster individually turns ferromagnetic below an ordering temperature which depends on its volume and Mn content.Comment: accepted for publication in Phys. Rev. Lett. (2006). High resolution images ibide

Minimal Cosmogenic Neutrinos

The observed flux of ultra-high energy (UHE) cosmic rays (CRs) guarantees the presence of high-energy cosmogenic neutrinos that are produced via photo-hadronic interactions of CRs propagating through intergalactic space. This flux of neutrinos doesn't share the many uncertainties associated with the environment of the yet unknown CR sources. Cosmogenic neutrinos have nevertheless a strong model dependence associated with the chemical composition, source distribution or evolution and maximal injection energy of UHE CRs. We discuss a lower limit on the cosmogenic neutrino spectrum which depends on the observed UHE CR spectrum and composition and relates directly to experimentally observable and model-independent quantities. We show explicit limits for conservative assumptions about the source evolution.Comment: 6 pages, 3 figure

Singularity in the boundary resistance between superfluid 4^4He and a solid surface

We report new measurements in four cells of the thermal boundary resistance $R$ between copper and $^4$He below but near the superfluid-transition temperature $T_\lambda$. For $10^{-7} \leq t \equiv 1 - T/T_\lambda \leq 10^{-4}$ fits of $R = R_0 t^{x_b} + B_0$ to the data yielded $x_b \simeq 0.18$, whereas a fit to theoretical values based on the renormalization-group theory yielded $x_b = 0.23$. Alternatively, a good fit of the theory to the data could be obtained if the {\it amplitude} of the prediction was reduced by a factor close to two. The results raise the question whether the boundary conditions used in the theory should be modified.Comment: 4 pages, 4 figures, revte