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The global transport of heat and momentum in turbulent convection is constrained by thin thermal and viscous boundary layers at the heated and cooled boundaries of the system. This bottle neck is thought to be lifted once the boundary layers them selves become fully turbulent at very high values of the Rayleigh number Ra—the dimensionless parameter that describes the vigor of convective turbulence. Laboratory experiments in cylindrical cells for Ra≳1012have reported different outcomes on the putative heat transport law. Here we show, by direct numerical simulations of three-dimensional turbulent Rayleigh–Bénard convection flows in a slender cylindrical cell of aspect ratio 1/10, that the Nusselt number—the dimensionless measure of heat transport—follows the classical power law of Nu=(0.0525±0.006)×Ra0.331±0.002up to Ra=1015. Intermittent fluctuations in the wall stress, a blue print of turbulence in the vicinity of the boundaries, manifest at all Ra considered here, increasing with increasing Ra, and suggest that an abrupt transition of the boundary layer to turbulence does not take place. [ABSTRACT FROM AUTHOR]

The global transport of heat and momentum in turbulent convection is constrained by thin thermal and viscous boundary layers at the heated and cooled boundaries of the system. This bottle neck is thought to be lifted once the boundary layers them selves become fully turbulent at very high values of the Rayleigh number Ra—the dimensionless parameter that describes the vigor of convective turbulence. Laboratory experiments in cylindrical cells for Ra≳1012have reported different outcomes on the putative heat transport law. Here we show, by direct numerical simulations of three-dimensional turbulent Rayleigh–Bénard convection flows in a slender cylindrical cell of aspect ratio 1/10, that the Nusselt number—the dimensionless measure of heat transport—follows the classical power law of Nu=(0.0525±0.006)×Ra0.331±0.002up to Ra=1015. Intermittent fluctuations in the wall stress, a blue print of turbulence in the vicinity of the boundaries, manifest at all Ra considered here, increasing with increasing Ra, and suggest that an abrupt transition of the boundary layer to turbulence does not take place. [ABSTRACT FROM AUTHOR]

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 107. 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. [ABSTRACT FROM AUTHOR]

The convection patterns that occur at and slightly above the onset of convection in cylindrical containers were determined as a function of aspect ratio, using simulations of Rayleigh-Bénard convection and linear stability analysis. The study focused primarily on aspect ratios 6 ≤ r ≤ 20, whereΓ= diameter/depth, with conducting or insulating, and no-slip boundary conditions and Prandtl numbers Pr = 0.7 and 28.9. Simulations demonstrate azimuthally pure Fourier mode patterns at onset consistent with what is expected from bifurcation theory, with an m = 1 mode, for even values ofΓ, and a concentric roll pattern, or m = 0 mode, for odd values ofΓ. For Rayleigh numbers slightly higher than onset other pure or mixed mode patterns were found and then for even higher Rayleigh numbers, straight parallel rolls were found. A linear stability analysis was used to determine the critical Rayleigh number, Rac, and flow pattern for a large range of aspect ratios and was found to agree with the simulation results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

We present high-resolution direct numerical simulation studies of turbulent Rayleigh–Bénard convection in a closed cylindrical cell with an aspect ratio of one. The focus of our analysis is on the finest scales of convective turbulence, in particular the statistics of the kinetic energy and thermal dissipation rates in the bulk and the whole cell. The fluctuations of the energy dissipation field can directly be translated into a fluctuating local dissipation scale which is found to develop ever finer fluctuations with increasing Rayleigh number. The range of these scales as well as the probability of high-amplitude dissipation events decreases with increasing Prandtl number. In addition, we examine the joint statistics of the two dissipation fields and the consequences of high-amplitude events. We have also investigated the convergence properties of our spectral element method and have found that both dissipation fields are very sensitive to insufficient resolution. We demonstrate that global transport properties, such as the Nusselt number, and the energy balances are partly insensitive to insufficient resolution and yield correct results even when the dissipation fields are under-resolved. Our present numerical framework is also compared with high-resolution simulations which use a finite difference method. For most of the compared quantities the agreement is found to be satisfactory. [ABSTRACT FROM AUTHOR]

An extreme dissipation event in the bulk of a closed three-dimensional turbulent convection cell is found to be correlated with a strong reduction of the large-scale circulation flow in the system that happens at the same time as a plume emission event from the bottom plate. The reduction in the large-scale circulation opens the possibility for a nearly frontal collision of down- and upwelling plumes and the generation of a high-amplitude thermal dissipation layer in the bulk. This collision is locally connected to a subsequent high-amplitude energy dissipation event in the form of a strong shear layer. Our analysis illustrates the impact of transitions in the large-scale structures on extreme events at the smallest scales of the turbulence, a direct link that is observed in a flow with boundary layers. We also show that detection of extreme dissipation events which determine the far-tail statistics of the dissipation fields in the bulk requires long-time integrations of the equations of motion over at least a hundred convective time units. [ABSTRACT FROM AUTHOR]