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The long-standing puzzle of diverging heat transport measurements at very high Rayleigh numbers (Ra) is addressed by a simple model based on well-known properties of classical boundary layers. The transition to the 'ultimate state' of convection in Rayleigh-Bénard cells is modeled as sub-critical transition controlled by the instability of large-scale boundary-layer eddies. These eddies are restricted in size either by the lateral wall or by the horizontal plates depending on the cell aspect ratio (in cylindrical cells, the cross-over occurs for a diameter-to-height ratio around 2 or 3). The large-scale wind known to settle across convection cells is assumed to have antagonist effects on the transition depending on its strength, leading to wind-immune, wind-hindered or wind-assisted routes to the ultimate regime. In particular winds of intermediate strength are assumed to hinder the transition by disrupting heat transfer, contrary to what is assumed in standard models. This phenomenological model is able to reconcile observations from more than a dozen of convection cells from Grenoble, Eugene, Trieste, Göttingen and Brno. In particular, it accounts for unexplained observations at high Ra, such as Prandtl number and aspect ratio dependences, great receptivity to details of the sidewall and differences in heat transfer efficiency between experiments.

Steady two-dimensional Rayleigh–Bénard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls with aspect ratios ${\\rm \\pi} /5\\leqslant \\varGamma \\leqslant 4{\\rm \\pi}$, where $\\varGamma$ is the width-to-height ratio for a pair of counter-rotating rolls, over eight orders of magnitude in the Rayleigh number, $10^3\\leqslant Ra\\leqslant 10^{11}$, and four orders of magnitude in the Prandtl number, $10^{-2}\\leqslant Pr\\leqslant 10^2$. At large $Ra$ where steady rolls are dynamically unstable, the computed rolls display $Ra \\rightarrow \\infty$ asymptotic scaling. In this regime, the Nusselt number $Nu$ that measures heat transport scales as $Ra^{1/3}$ uniformly in $Pr$. The prefactor of this scaling depends on $\\varGamma$ and is largest at $\\varGamma \\approx 1.9$. The Reynolds number $Re$ for large-$Ra$ rolls scales as $Pr^{-1} Ra^{2/3}$ with a prefactor that is largest at $\\varGamma \\approx 4.5$. All of these large-$Ra$ features agree quantitatively with the semi-analytical asymptotic solutions constructed by Chini & Cox (Phys. Fluids, vol. 21, 2009, 083603). Convergence of $Nu$ and $Re$ to their asymptotic scalings occurs more slowly when $Pr$ is larger and when $\\varGamma$ is smaller.

In this paper, we describe the recent developments in the field of buoyancy-driven turbulence with a focus on energy spectrum and flux. Scaling and numerical arguments show that the stably-stratified turbulence with moderate stratification has kinetic energy spectrum E u ( k ) ∼ k − 11 5 and the kinetic energy flux u ( k ) ∼ k − 4 5 , which is called Bolgiano-Obukhov scaling. However, for Prandtl number near unity, the energy flux for the three-dimensional Rayleigh-Bénard convection (RBC) is approximately constant in the inertial range that results in Kolmorogorv's spectrum ( E u ( k ) ∼ k − 5 3 ) for the kinetic energy. The phenomenology of RBC should apply to other flows where the buoyancy feeds the kinetic energy, e.g. bubbly turbulence and fully-developed Rayleigh Taylor instability. This paper also covers several models that predict the Reynolds and Nusselt numbers of RBC. Recent works show that the viscous dissipation rate of RBC scales as ∼ Ra 1.3 , where Ra is the Rayleigh number.

Turbulent superstructures in horizontally extended three-dimensional Rayleigh–Bénard convection flows are investigated in controlled laboratory experiments in water at Prandtl number ${Pr}=7$. A Rayleigh–Bénard cell with square cross-section, aspect ratio $\\varGamma =l/h=25$, side length $l$ and height $h$ is used. Three different Rayleigh numbers in the range $10^{5} < {Ra} < 10^{6}$ are considered. The cell is accessible optically, such that thermochromic liquid crystals can be seeded as tracer particles to monitor simultaneously temperature and velocity fields in a large section of the horizontal mid-plane for long time periods of up to 6 h, corresponding to approximately $10^{4}$ convective free-fall time units. The joint application of stereoscopic particle image velocimetry and thermometry opens the possibility to assess the local convective heat flux fields in the bulk of the convection cell and thus to analyse the characteristic large-scale transport patterns in the flow. A direct comparison with existing direct numerical simulation data in the same parameter range of $Pr$, ${Ra}$ and $\\varGamma$ reveals the same superstructure patterns and global turbulent heat transfer scaling ${Nu}({Ra})$. Slight quantitative differences can be traced back to violations of the isothermal boundary condition at the extended water-cooled glass plate at the top. The characteristic scales of the patterns fall into the same size range, but are systematically larger. It is confirmed experimentally that the superstructure patterns are an important backbone of the heat transfer. The present experiments enable, furthermore, the study of the gradual evolution of the large-scale patterns in time, which is challenging in simulations of large-aspect-ratio turbulent convection.

The Rayleigh wave meta-Rayleigh scattering on a three-dimensional deterministic roughness of an isotropic solid is obtained. It violates and expands the fundamental conception of the Rayleigh law of scattering and is described by the new topological laws in the Rayleigh limit, obtained in the present work. It gives the new principal physical results, enabling the construction of arbitrary arbitrary frequency and angular spectrum of scattering through its meta-Rayleigh modulation by a roughness structure in two independent space dimensions in the Rayleigh limit.

Turbulent Rayleigh-Bénard convection displays a large-scale order in the form of rolls and cells on lengths larger than the layer height once the fluctuations of temperature and velocity are removed. These turbulent superstructures are reminiscent of the patterns close to the onset of convection. Here we report numerical simulations of turbulent convection in fluids at different Prandtl number ranging from 0.005 to 70 and for Rayleigh numbers up to 10 7 . We identify characteristic scales and times that separate the fast, small-scale turbulent fluctuations from the gradually changing large-scale superstructures. The characteristic scales of the large-scale patterns, which change with Prandtl and Rayleigh number, are also correlated with the boundary layer dynamics, and in particular the clustering of thermal plumes at the top and bottom plates. Our analysis suggests a scale separation and thus the existence of a simplified description of the turbulent superstructures in geo- and astrophysical settings. Turbulent fluids in nature, counter-intuitively, can exhibit large-scale order that persists for long times. Pandey et al. numerically characterize the formation of these superstructures in turbulent convection by separating the fast motions at small-scales from those that gradually vary at large scales.

Distributed acoustic sensing techniques based on Rayleigh scattering have been widely used in many applications due to their unique advantages, such as long-distance detection, high spatial resolution, and wide sensing bandwidth. In this paper, we provide a review of the recent advancements in distributed acoustic sensing techniques. The research progress and operation principles are systematically reviewed. The pivotal technologies and solutions applied to distributed acoustic sensing are introduced in terms of polarization fading, coherent fading, spatial resolution, frequency response, signal-to-noise ratio, and sensing distance. The applications of the distributed acoustic sensing are covered, including perimeter security, earthquake monitoring, energy exploration, underwater positioning, and railway monitoring. The potential developments of the distributed acoustic sensing techniques are also discussed.

Statistical properties of turbulent Rayleigh–Bénard convection at low Prandtl numbers $Pr$ , which are typical for liquid metals such as mercury or gallium ( $Pr\\simeq 0.021$ ) or liquid sodium ( $Pr\\simeq 0.005$ ), are investigated in high-resolution three-dimensional spectral element simulations in a closed cylindrical cell with an aspect ratio of one and are compared to previous turbulent convection simulations in air for $Pr=0.7$ . We compare the scaling of global momentum and heat transfer. The scaling exponent $\\unicode[STIX]{x1D6FD}$ of the power law $Nu=\\unicode[STIX]{x1D6FC}Ra^{\\unicode[STIX]{x1D6FD}}$ is $\\unicode[STIX]{x1D6FD}=0.265\\pm 0.01$ for $Pr=0.005$ and $\\unicode[STIX]{x1D6FD}=0.26\\pm 0.01$ for $Pr=0.021$ , which are smaller than that for convection in air ( $Pr=0.7$ , $\\unicode[STIX]{x1D6FD}=0.29\\pm 0.01$ ). These exponents are in agreement with experiments. Mean profiles of the root-mean-square velocity as well as the thermal and kinetic energy dissipation rates have growing amplitudes with decreasing Prandtl number, which underlies a more vigorous bulk turbulence in the low- $Pr$ regime. The skin-friction coefficient displays a Reynolds number dependence that is close to that of an isothermal, intermittently turbulent velocity boundary layer. The thermal boundary layer thicknesses are larger as $Pr$ decreases and conversely the velocity boundary layer thicknesses become smaller. We investigate the scaling exponents and find a slight decrease in exponent magnitude for the thermal boundary layer thickness as $Pr$ decreases, but find the opposite case for the velocity boundary layer thickness scaling. A growing area fraction of turbulent patches close to the heating and cooling plates can be detected by exceeding a locally defined shear Reynolds number threshold. This area fraction is larger for lower $Pr$ at the same $Ra$ , but the scaling exponent of its growth with Rayleigh number is reduced. Our analysis of the kurtosis of the locally defined shear Reynolds number demonstrates that the intermittency in the boundary layer is significantly increased for the lower Prandtl number and for sufficiently high Rayleigh number compared to convection in air. This complements our previous findings of enhanced bulk intermittency in low-Prandtl-number convection.

As the separation between two emitters is decreased below the Rayleigh limit, the information that can be gained about their separation using traditional imaging techniques, photon counting in the image plane, reduces to nil. Assuming the sources are of equal intensity, Rayleigh's 'curse' can be alleviated by making phase-sensitive measurements in the image plane. However, with unequal and unknown intensities the curse returns regardless of the measurement, though the ideal scheme would still outperform image plane counting (IPC), i.e. recording intensities on a screen. We analyze the limits of the super-resolved position localization by inversion of coherence along an edge (SPLICE) phase measurement scheme as the intensity imbalance between the emitters grows. We find that SPLICE still outperforms IPC for moderately disparate intensities. For larger intensity imbalances we propose a hybrid of IPC and SPLICE, which we call 'adapted SPLICE', requiring only simple modifications. Using Monte Carlo simulation, we identify regions (emitter brightness, separation, intensity imbalance) where it is advantageous to use SPLICE over IPC, and when to switch to the adapted SPLICE measurement. We find that adapted SPLICE can outperform IPC for large intensity imbalances, e.g. 10 000:1, with the advantage growing with greater disparity between the two intensities. Finally, we also propose additional phase measurements for estimating the statistical moments of more complex source distributions. Our results are promising for implementing phase measurements in sub-Rayleigh imaging tasks such as exoplanet detection.