Turbulent rotating convection at high Rayleigh and Taylor numbers

Niemela, Joseph; Babuin, Simone; Sreenivasan, Katepalli R.

doi:10.1017/s0022112009994101

Cited by 49 publications

(41 citation statements)

References 24 publications

(34 reference statements)

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“…This force acts in the circumferential direction only and may qualitatively alter the flow from a condition of a domain filling large-scale circulation (at low constant rotation rates) or dispersed local thermal plumes (at high constant rotation rates), to a more or less segregated situation in which a pronounced thermal column forms along the centreline of the domain and highly sheared structures appear in the boundary layer near the vertical sidewalls. Situations displaying this thermal column were found to support a strongly increased Nusselt number, indicating a striking qualitative similarity with findings from the experimental work reported in Niemela et al (2010). The experimental work was conducted at different flow conditions, e.g., a higher Rayleigh number and a different Prandtl number, which are currently not accessible for DNS.…”

Section: Discussionsupporting

confidence: 77%

“…Such an increase in the Nusselt number at appropriate Rossby numbers is due to Ekman pumping, which is efficient only for r > 1 and is gradually reduced once the Rayleigh number is increased . Hence the study by Niemela et al (2010) has revealed a reduction of Nu under rotation: in liquid helium at r ¼ 0:7 and at very high Ra $ Oð10 11 À 10 15 Þ there is no effective Ekman pumping, while the damping of vertical motion by rotation is already felt.…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

“…A first, unique physical experiment was carried out by Niemela et al (2010) producing interesting results (Niemela et al, 2010). Heat transport measurements at constant as well as at periodically varied rotation rates were conducted in a wide range of physical conditions, with cryogenic helium gas as working fluid.…”

Section: Introductionmentioning

confidence: 99%

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Intensified heat transfer in modulated rotating Rayleigh–Bénard convection

Geurts

Kunnen

2014

International Journal of Heat and Fluid Flow

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Section: Discussionsupporting

confidence: 77%

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

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Intensified heat transfer in modulated rotating Rayleigh–Bénard convection

Geurts

Kunnen

2014

International Journal of Heat and Fluid Flow

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“…Of recent interest in these studies have been transitions between rotationally dominated and nonrotating turbulent states (2-10) and the enhancement of heat transport by rotation (6,8,(11)(12)(13)(14)(15). Numerical simulations of planetary dynamo action by rotating convection also concentrate on fluids with unit order Pr (16).…”

mentioning

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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“…In comparison to numerous studies of RC in moderate Prandtl number fluids [11,13,14,20,23,[63][64][65][66][67][68][69][70], only a rather limited number of rotating convection investigations have been made in low Prandtl number fluids [18][19][20]51,71]. The governing equations for rotating convection are i.e., the angular velocity Ω = 0.84 rad/s and the rotation period P Ω = 7.5 s. The height of the layer is fixed at H = 10 cm.…”

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 rotating convection at high Rayleigh and Taylor numbers

Cited by 49 publications

References 24 publications

Intensified heat transfer in modulated rotating Rayleigh–Bénard convection

Intensified heat transfer in modulated rotating Rayleigh–Bénard convection

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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