Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Abstract

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...

A heuristic framework for next-generation models of geostrophic convective turbulence

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Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection

“…Recent research progress on low-Prandtl number convection includes Vogt et al's 10 discovery that large-scale circulation takes the form of a jump rope vortex in cells of aspect ratio higher than unity when using liquid gallium as the working fluid. Schumacher et al 11 found that the generation of small-scale vorticity in the bulk convection follows the same mechanisms as idealized isotropic turbulence for low-Prandtl number convection. Scheel and Schumacher 2 identified a transition between the rotationally constrained and the weakly rotating turbulent states in rotating Rayleigh-Bénard convection with liquid gallium that differs substantially from moderate-Prandtl number convection.…”

“…Scheel and Schumacher 2 identified a transition between the rotationally constrained and the weakly rotating turbulent states in rotating Rayleigh-Bénard convection with liquid gallium that differs substantially from moderate-Prandtl number convection. The main differences are due to the more diffuse temperature field, more vigorous velocity field, and coarser yet fewer production of thermal plumes in low-Prandtl number convection [11][12][13] .…”

Predicting transition ranges to fully turbulent viscous boundary layers in low Prandtl number convection flows

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