Turbulent Rayleigh–Bénard convection in low Prandtl–number fluids

Horanyi, S.; Krebs, L.; Müller, Ulrich

doi:10.1016/s0017-9310(99)00059-9

Cited by 58 publications

(67 citation statements)

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“…In some recent experiments, however, Ciliberto, Cioni & Laroche (1996) have found that the Nusselt number in water does not change when screens are placed inside the domain so that the recirculation cell is destroyed. This would suggest that in the high P r regime the large-scale motion is ineffective in the heat Kerr (1996) at P r = 0.7; •, experimental results by Cioni et al (1997) at P r = 0.025; , experimental results by Cioni et al (1997) and by Chillá et al (1993) at P r = 4.0; , experimental results by Horanyi et al (1997) at P r = 0.005; , fit Nu ∼ Ra 0.285 ; , fit Nu ∼ Ra 0.25 ; , fit Nu ∼ Ra 0.25 . (b) Nu vs. P r relation at Ra = 6 × 10 5 :…”

Section: Resultsmentioning

confidence: 99%

Prandtl number effects in convective turbulence

1999

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It has recently been recognized that the convective velocities achieved in the current solar convection simulations might be overestimated. The newly-revealed effects of the prevailing small-scale magnetic field within the convection zone may offer possible solutions to this problem. The small-scale magnetic fields can reduce the convective amplitude of small-scale motions through the Lorentz-force feedback, which concurrently inhibits the turbulent mixing of entropy between upflows and downflows. As a result, the effective Prandtl number may exceed unity inside the solar convection zone. In this paper, we propose and numerically confirm a possible suppression mechanism of convective velocity in the effectively high-Prandtl number regime. If the effective horizontal thermal diffusivity decreases (the Prandtl number accordingly increases), the subadiabatic layer which is formed near the base of the convection zone by continuous depositions of low entropy transported by adiabatically downflowing plumes is enhanced and extended. The global convective amplitude in the high-Prandtl thermal convection is thus reduced especially in the lower part of the convection zone via the change in the mean entropy profile which becomes more subadiabatic near the base and less superadiabatic in the bulk.

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Section: Resultsmentioning

confidence: 99%

Prandtl number effects in convective turbulence

1999

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“…This difference has been observed previously (e.g., refs. 23,25,34,36). The inertial scaling illustrates the dominant role of interior turbulence in liquid metal convection.…”

Section: Methodsmentioning

confidence: 95%

“…23,25,36). Essentially, the difference between scaling laws [1] and [4] is that in the former the thermal boundary layer thickness is determined by its own marginal stability, whereas in the latter the thermal boundary layer thickness is set by the strength of interior turbulence.…”

Section: Heat Transfer Regimesmentioning

confidence: 99%

Turbulent convection in liquid metal with and without rotation

King

Aurnou

2013

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

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The magnetic fields of Earth and other planets are generated by turbulent, rotating convection in liquid metal. Liquid metals are peculiar in that they diffuse heat more readily than momentum, quantified by their small Prandtl numbers, Pr = 1. Most analog models of planetary dynamos, however, use moderate Pr fluids, and the systematic influence of reducing Pr is not well understood. We perform rotating Rayleigh-Bénard convection experiments in the liquid metal gallium (Pr = 0:025) over a range of nondimensional buoyancy forcing (Ra) and rotation periods (E). Our primary diagnostic is the efficiency of convective heat transfer (Nu). In general, we find that the convective behavior of liquid metal differs substantially from that of moderate Pr fluids, such as water. In particular, a transition between rotationally constrained and weakly rotating turbulent states is identified, and this transition differs substantially from that observed in moderate Pr fluids. This difference, we hypothesize, may explain the different classes of magnetic fields observed on the Gas and Ice Giant planets, whose dynamo regions consist of Pr < 1 and Pr > 1 fluids, respectively.T he interiors of Earth and other terrestrial bodies, as well as the Gas Giant planets, contain vast oceans of flowing metals. Mixed by turbulent convection as these planets cool, the flowing conductors produce electric currents that maintain planetary magnetic fields. These bodies also rotate, and it is expected that the resulting Coriolis forces strongly influence convective dynamo processes. Beyond linear theory (1), however, not much is known about the dynamics of rotating convection in liquid metal that underlie planetary magnetic field generation.Theory and experiments often focus on a simplified analog of geophysical and astrophysical systems, Rayleigh-Bénard convection (RBC). The RBC system consists of a fluid layer contained between flat, horizontal plates separated by distance h, the bottom of which is warmer than the top by ΔT, and with downward pointing gravity, g. Near the bottom boundary, the fluid warms and expands by a volumetric factor α (per degree kelvin) and similarly cools and contracts near the top boundary, such that the fluid is unstably stratified.Rotating convection is explored by spinning the RBC system about a vertical axis at an angular rate Ω, which is adopted as the reference frame for the model. The fluid dynamics of the system are characterized by three dimensionless parameters. The Prandtl number, Pr ≡ ν=κ, defines the diffusive transport properties of the fluid, where ν and κ are its viscous and thermal diffusivities. The Rayleigh number, Ra ≡ αgΔTh 3 =ðνκÞ, prescribes the magnitude of the buoyancy force. Finally, the rotation period is specified by the Ekman number, E ≡ ν=ð2Ωh 2 Þ. The primary diagnostic used in many convection studies, including this one, is the Nusselt number, which characterizes the efficiency of heat transport by convection as Nu ≡ qh=ðkΔTÞ, where q is total heat flux and k is the fluid's thermal conductivi...

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“…As shown in Figure 7d, this large-scale axisymmetric, inertial circulation (with power dominantly at m = 0 and subdominantly at m = 4) generates similarly strong horizontal temperature gradients on the mid-plane of the fluid, again, approaching 60% of the imposed vertical temperature gradient. The decrease in dominant horizontal mode number from m = 3 in case RBC 1 n to the axisymmetric mode in case RBC 2 n is reminiscent of the inferred change in mode number in the Γ = 4.5 liquid sodium convection study of [53]. n , which has the highest Ra value and relatively low aspect ratio of Γ = 2, yields a classical large-scale circulation (LSC), with a single non-axisymmetric m = 1 inertial cell dominating the fluid domain [55][56][57].…”

Section: Resultsmentioning

confidence: 79%

“…In fact, experiments in liquid metals have yielded a wide range of results providing α values from 1/5 up to 1/3 [18,20,[51][52][53][54]. This broad range of possible α values shows that heat transfer in liquid metals is not as well understood as it is in moderate P r fluids [16].…”

Section: Essential Theorymentioning

confidence: 99%

Canonical Models of Geophysical and Astrophysical Flows: Turbulent Convection Experiments in Liquid Metals

Ribeiro¹,

Fabre²,

Guermond³

et al. 2015

Metals

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Planets and stars are often capable of generating their own magnetic fields. This occurs through dynamo processes occurring via turbulent convective stirring of their respective molten metal-rich cores and plasma-based convection zones. Present-day numerical models of planetary and stellar dynamo action are not carried out using fluids properties that mimic the essential properties of liquid metals and plasmas (e.g., using fluids with thermal Prandtl numbers P r < 1 and magnetic Prandtl numbers P m 1). Metal dynamo simulations should become possible, though, within the next decade. In order then to understand the turbulent convection phenomena occurring in geophysical or astrophysical fluids and next-generation numerical models thereof, we present here canonical, end-member examples of thermally-driven convection in liquid gallium, first with no magnetic field or rotation present, then with the inclusion of a background magnetic field and then in a rotating system (without an imposed magnetic field). In doing so, we demonstrate the essential behaviors of convecting liquid metals that are necessary for building, as well as benchmarking, accurate, robust models of magnetohydrodynamic processes in P m P r < 1 geophysical and astrophysical systems. Our study results also show strong agreement between laboratory and numerical experiments, demonstrating that high resolution numerical simulations can be made capable of modeling the liquid metal convective turbulence needed in accurate next-generation dynamo models.

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Turbulent Rayleigh–Bénard convection in low Prandtl–number fluids

Cited by 58 publications

References 50 publications

Prandtl number effects in convective turbulence

Prandtl number effects in convective turbulence

Turbulent convection in liquid metal with and without rotation

Canonical Models of Geophysical and Astrophysical Flows: Turbulent Convection Experiments in Liquid Metals

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