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.

We discuss two aspects of turbulent Rayleigh-Bénard convection (RBC) on the basis of highresolution direct numerical simulations in a unique setting; a closed cylindrical cell of aspect ratio of one. First, we present a comprehensive comparison of statistical quantities such as energy dissipation rates and boundary layer thickness scales. Data are used from three simulation run series at Prandtl numbers P r that cover two orders of magnitude. In contrast to most previous studies in RBC the focus of the present work is on convective turbulence at very low Prandtl numbers including P r = 0.021 for liquid mercury or gallium and P r = 0.005 for liquid sodium. In this parameter range of RBC, inertial effects cause a dominating turbulent momentum transport that is in line with highly intermittent fluid turbulence both in the bulk and in the boundary layers and thus should be able to trigger a transition to the fully turbulent boundary layers of the ultimate regime of convection for higher Rayleigh number. Secondly, we predict the ranges of Rayleigh numbers for which the viscous boundary layer will transition to turbulence and the flow as a whole will cross over into the ultimate regime. These transition ranges are obtained by extrapolation from our simulation data. The extrapolation methods are based on the large-scale properties of the velocity profile. Two of the three methods predict similar ranges for the transition to ultimate convection when their uncertainties are taken into account. All three extrapolation methods indicate that the range of critical Rayleigh numbers Rac is shifted to smaller magnitudes as the Prandtl number becomes smaller.

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The entrainment of clear air and its subsequent mixing with a filament of cloudy air, as occurs at the edge of a cloud, is studied in three-dimensional direct numerical simulations that combine the Eulerian description of the turbulent velocity, temperature, and vapor fields with a Lagrangian cloud droplet ensemble. Forced and decaying turbulence is considered, such as when the dynamics around the filament is driven by larger-scale eddies or during the final period of the life cycle of a cloud. The microphysical response depicted in n d 2 hr 3 i space (where n d and r are droplet number density and radius, respectively) shows characteristics of both homogeneous and inhomogeneous mixing, depending on the Damk€ ohler number. The transition from inhomogeneous to homogeneous mixing leads to an offset of the homogeneous mixing curve to larger dilution fractions. The response of the system is governed by the smaller of the single droplet evaporation time scale and the bulk phase relaxation time scale. Variability within the n d 2 hr 3 i space increases with decreasing sample volume, especially during the mixing transients. All of these factors have implications for the interpretation of measurements in clouds. The qualitative mixing behavior changes for forced versus decaying turbulence, with the latter yielding remnant patches of unmixed cloud and stronger fluctuations. Buoyancy due to droplet evaporation is observed to play a minor role in the mixing for the present configuration. Finally, the mixing process leads to the transient formation of a pronounced nearly exponential tail of the probability density function of the Lagrangian supersaturation, and a similar tail emerges in the droplet size distribution under inhomogeneous conditions.

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 bottleneck is thought to be lifted once the boundary layers themselves become fully turbulent at very high values of the Rayleigh numberRa—the dimensionless parameter that describes the vigor of convective turbulence. Laboratory experiments in cylindrical cells forRa≳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 ratio1/10, that the Nusselt number—the dimensionless measure of heat transport—follows the classical power law ofNu=(0.0525±0.006)×Ra0.331±0.002up toRa=1015. Intermittent fluctuations in the wall stress, a blueprint of turbulence in the vicinity of the boundaries, manifest at allRaconsidered here, increasing with increasingRa, and suggest that an abrupt transition of the boundary layer to turbulence does not take place.