New perspectives in turbulent Rayleigh-Bénard convection

Chillà, Francesca; Schumacher, Jöerg

doi:10.1140/epje/i2012-12058-1

Cited by 666 publications

(584 citation statements)

References 190 publications

(370 reference statements)

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“…and γ is an exponent that depends on the convective regime (e.g., see Chillà and Schumacher 2012), the boundary layer ratio parameter may be defined as…”

Section: Methodsmentioning

confidence: 99%

A rotating annulus driven by localized convective forcing: a new atmosphere-like experiment

Scolan

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2017

Exp Fluids

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unstable flows which are qualitatively similar to those previously observed in the classical thermally driven annulus. However, in contrast to the classical configuration, they typically exhibit more spatio-temporal complexity. Thus, several regimes of flow demonstrate the equilibrated coexistence of, and interaction between, free convection and baroclinic wave modes. These new features were not previously observed in the classical annulus and validate the new setup as a tool for exploring fundamental atmosphere-like dynamics in a more realistic framework. Thermal structure in the fluid is investigated and found to be qualitatively consistent with previous numerical results, with nearly isothermal conditions, respectively, above and below the heat source and sink, and stably-stratified, sloping isotherms in the near-adiabatic interior.

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“…and γ is an exponent that depends on the convective regime (e.g., see Chillà and Schumacher 2012), the boundary layer ratio parameter may be defined as…”

Section: Methodsmentioning

confidence: 99%

A rotating annulus driven by localized convective forcing: a new atmosphere-like experiment

Scolan

Read

2017

Exp Fluids

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“…The Reynolds number is Re = u rms H=ν and the Nusselt number is Nu = 1 + ðRa PrÞ 1=2 hwT i V,t . The Kolmogorov and Bolgiano lengths follow from [6] and thermal boundary layer thickness from [2]. implies that the majority of kinetic energy is injected in the range r > δ T , i.e., at the larger scales, and that the low-Prandtl flow is thus closer to the classical Kolmogorov turbulence, at least for ℓ K δ T .…”

Section: Turbulent Cascade and Scale-resolved Energy Injectionmentioning

confidence: 97%

“…Above the Bolgiano scale, the turbulent motion should be dominated by the large-scale circulation that is initiated and sustained by the largest thermal plumes (2). Below the Bolgiano scale convection is expected to be similar to classical Kolmogorov-like fluid turbulence (27).…”

Section: Turbulent Cascade and Scale-resolved Energy Injectionmentioning

confidence: 99%

“…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)(4)(5).…”

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confidence: 99%

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

Schumacher

Götzfried

Scheel

2015

Proc. Natl. Acad. Sci. U.S.A.

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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...

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“…Convective flows are usually studied by using a simple model, i.e. Rayleigh-Bénard convection, the flow in a layer heated from below and cooled from above (Ahlers, Grossmann & Lohse 2009;Lohse & Xia 2010;Chillà & Schumacher 2012;Xia 2013). For intermediate and high Prandtl number convection, which covers the geophysical flows mentioned above, heat is transported mainly by small-scale structures known as plumes.…”

Section: Introductionmentioning

confidence: 99%

Mixed thermal conditions in convection: how do continents affect the mantle’s circulation?

Ostilla–Mónico

2017

J. Fluid Mech.

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Natural convection is omnipresent on Earth. A basic and well-studied model for it is Rayleigh-Bénard convection, the fluid flow in a layer heated from below and cooled from above. Most explorations of Rayleigh-Bénard convection focus on spatially uniform, perfectly conducting thermal boundary conditions, but many important geophysical phenomena are characterized by boundary conditions which are a mixture of conducting and adiabatic materials. For example, the differences in thermal conductivity between continental and oceanic lithospheres are believed to play an important role in plate tectonics. To study this, Wang et al. (J. Fluid Mech., vol. 817, 2017, R1), measure the effect of mixed adiabatic-conducting boundary conditions on turbulent Rayleigh-Bénard convection, finding experimental proof that even if the total heat transfer is primarily affected by the adiabatic fraction, the arrangement of adiabatic and conducting plates is crucial in determining the large-scale flow dynamics.

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New perspectives in turbulent Rayleigh-Bénard convection

Cited by 666 publications

References 190 publications

A rotating annulus driven by localized convective forcing: a new atmosphere-like experiment

A rotating annulus driven by localized convective forcing: a new atmosphere-like experiment

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

Mixed thermal conditions in convection: how do continents affect the mantle’s circulation?

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