Prandtl-, Rayleigh-, and Rossby-Number Dependence of Heat Transport in Turbulent Rotating Rayleigh-Bénard Convection

Zhong, Jin-Qiang; Stevens, Richard J. A. M.; Clercx, Hjh Herman; Verzicco, Roberto; Lohse, Detlef; Ahlers, Guenter

doi:10.1103/physrevlett.102.044502

Cited by 145 publications

(259 citation statements)

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“…Previous experimental [7]- [13] and numerical studies [11]- [16] at constant Ra and Pr have shown that at moderate rotation rates the convective heat transfer is higher than for the nonrotating case. This heat transport enhancement with respect to the non-rotating case has been ascribed to Ekman pumping [8], [10]- [13], [15]- [18].…”

mentioning

confidence: 99%

“…Here we choose the latter since Ro indicates when Ekman pumping effects become important with respect to buoyancy effects [12]. In [11] it was shown that no heat transfer enhancement is observed at small Pr 0.7. This was explained by the larger thermal diffusivity at lower Pr, as a result of which the heat that is carried by the vertical vortices created by Ekman pumping spreads out in the middle of the cell.…”

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confidence: 99%

“…Corresponding phenomena occur at the upper boundary. This process depends strongly on Ra and Pr [11] and the boundary conditions [19]. Liu and Ecke [7] showed that this increase in Nu can be presented in several ways, as the rotation rate can be expressed by the Taylor Ta number, which measures the effect of the rotational Coriolis force, and the Rossby Ro number, which indicates the relation between the buoyancy and Coriolis forces.…”

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confidence: 99%

“…The numerical details concerning rotating RB convection are described in detail in [11,12]. Most simulations were performed on a grid of 129 × 257 × 257 nodes, respectively, in the radial, azimuthal and vertical directions, allowing for a sufficient resolution of the small scales both inside the bulk of turbulence and in the BLs (where the grid-point density has been enhanced) for the parameters employed here [11,12]. Nu is calculated in several ways, as described in detail in [23], and its statistical convergence has been controlled.…”

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Optimal Prandtl number for heat transfer in rotating Rayleigh–Bénard convection

2010

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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).…”

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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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2012

Rotating Thermal Flows in Natural and Industrial Processes

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Prandtl-, Rayleigh-, and Rossby-Number Dependence of Heat Transport in Turbulent Rotating Rayleigh-Bénard Convection

Cited by 145 publications

References 25 publications

Optimal Prandtl number for heat transfer in rotating Rayleigh–Bénard convection

Optimal Prandtl number for heat transfer in rotating Rayleigh–Bénard convection

Turbulent convection in liquid metal with and without rotation

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