Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr = 0.7 and in liquid mercury at Pr = 0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large-and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Our results have thus interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications. T urbulent convection depends strongly on the material properties of the working fluid that are quantified by the Prandtl number, the ratio of kinematic viscosity of the fluid to thermal diffusivity of the temperature, Pr = ν=κ. Compared with the vast number of investigations at Pr ≥ 1 (1, 2), the very-low-Pr regime appears almost as a "terra incognita" despite many applications. Turbulent convection in the Sun is present at Prandtl numbers Pr < 10 −3 (3-5). The Prandtl number in the liquid metal core of the Earth is Pr ∼ 10 −2 (6). Convection in material processing (7), nuclear engineering (8), or liquid metal batteries (9) has Prandtl numbers between 3 × 10 −2 and 10 −3 . Rayleigh-Bénard convection (RBC), a fluid flow in a layer that is cooled from above and heated from below, is a paradigm for all of these examples. One reason for significantly fewer low-Pr RBC studies is that laboratory measurements have to be conducted in opaque liquid metals such as mercury or gallium at Pr = 0.021 (10-12). The lowest value for a Prandtl number that can be obtained in optically transparent fluids is Pr = 0.2 for binary gas mixtures (13), i.e., an order of magnitude larger than in liquid metals. Direct numerical simulations (DNS) are currently the only way to gain access to the full 3D convective turbulent fields in low-Pr convection (14-18). These simulations turn out to become very demanding if the...

The dynamics and lifetime of atmospheric clouds are tightly coupled to entrainment and turbulent mixing. This paper presents direct numerical simulations of turbulent mixing followed by droplet evaporation at the cloud‐clear air interface in a meter‐sized volume, with an ensemble of up to almost half a billion individual cloud water droplets. The dependence of the mixing process on domain size reveals that inhomogeneous mixing becomes increasingly important as the domain size is increased. The shape of the droplet size distribution varies strongly with spatial scale, with the appearance of a pronounced negative exponential tail. The increase of relative dispersion during the transient mixing process is strongly dependent on the scale of the mixing and therefore on the Damköhler number, defined as the turbulence large‐eddy time scale divided by the cloud supersaturation relaxation time.

Three-dimensional direct numerical simulations of a shearless mixing layer in a small fraction of the cloud–clear air interface are performed to study the response of an ensemble of cloud water droplets to the turbulent entrainment of clear air into a cloud filament. The main goal of this work is to understand how mixing of cloudy and clear air evolves as turbulence and thermodynamics interact through phase changes, and how the cloud droplets respond. In the main simulation case, mixing proceeds between a higher level of turbulence in the cloudy filament and a lower level of turbulence in the clear air environment – the typical shearless mixing layer set-up. Fluid turbulence is driven solely by buoyancy, which incorporates feedbacks from the temperature, the vapour content and the liquid water content fields. Two different variations on the core set of shearless mixing layer simulations are discussed, a simulation in a larger domain and a simulation with the same turbulence level inside the filament and its environment. Overall, it is found that, as evaporation occurs for the droplets that enter subsaturated clear air regions, buoyancy comes to dominate the subsequent evolution of the mixing layer. The buoyancy feedback leads initially to downdraughts at the cloudy–clear air interface and to updraughts in the bulk regions. The strength of the turbulence after initial transients depends on the domain size, showing that the range of scales is an important parameter in the shearless mixing layer set-up. In contrast, the level of turbulence in the clear air is found to have little effect on the evolution of the mixing process. The distributions of cloud water droplet size, supersaturation at the droplet positions and vertical velocity are more sensitive to domain size than to the details of the turbulence profile, suggesting that the evolution of cloud microphysics is more sensitive to large-scale as opposed to small-scale properties of the flow.

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