On the triggering of the Ultimate Regime of convection

Roche, Philippe-Emmanuel; Gauthier, Frédéric; Kaiser, Robert; Salort, Julien

doi:10.1088/1367-2630/12/8/085014

Cited by 118 publications

(207 citation statements)

References 42 publications

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“…As a final remark, we can stress that the effect is small for sufficiently high Rayleigh numbers. The smallness of the effect is not really surprising; it is in good agreement with several other measurements [50,[90][91][92] in which the large scale flow has been disturbed or clearly suppressed and in which the Nusselt number has been found to vary by at most 5%.…”

Section: Nu-ra Scalingsupporting

confidence: 90%

New perspectives in turbulent Rayleigh-Bénard convection

2012

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Abstract. Recent experimental, numerical and theoretical advances in turbulent Rayleigh-Bénard convection are presented. Particular emphasis is given to the physics and structure of the thermal and velocity boundary layers which play a key role for the better understanding of the turbulent transport of heat and momentum in convection at high and very high Rayleigh numbers. We also discuss important extensions of Rayleigh-Bénard convection such as non-Oberbeck-Boussinesq effects and convection with phase changes.

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Section: Nu-ra Scalingsupporting

confidence: 90%

New perspectives in turbulent Rayleigh-Bénard convection

2012

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“…Other experimental results have indicated departure from the trend in Fig. 2 at Ra > 10 11 [28] or Ra > 10 12 -10 13 [29]. Our results are not significantly different from the latter of these.…”

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confidence: 66%

Completing the Mechanical Energy Pathways in Turbulent Rayleigh-Bénard Convection

2013

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A new, more complete view of the mechanical energy budget for Rayleigh-Bénard convection is developed and examined using three-dimensional numerical simulations at large Rayleigh numbers and Prandtl number of 1. The driving role of available potential energy is highlighted. The relative magnitudes of different energy conversions or pathways change significantly over the range of Rayleigh numbers Ra $ 10 7 -10 13 . At Ra < 10 7 small-scale turbulent motions are energized directly from available potential energy via turbulent buoyancy flux and kinetic energy is dissipated at comparable rates by both the largeand small-scale motions. In contrast, at Ra ! 10 10 most of the available potential energy goes into kinetic energy of the large-scale flow, which undergoes shear instabilities that sustain small-scale turbulence. The irreversible mixing is largely confined to the unstable boundary layer, its rate exactly equal to the generation of available potential energy by the boundary fluxes, and mixing efficiency is 50%. Introduction.-Flow in a horizontal layer of fluid heated uniformly from below and cooled from above-RayleighBénard convection (RBC)-is an idealized problem from which much can be learned about the nature of convective flow and heat transfer. Recent attention has focused on the relative importance of the boundary layer and interior behavior, including flow structures, at very large Rayleigh numbers [1][2][3][4][5][6]. The salient features of the flow can be usefully interpreted in terms of the energy budget, and previous work has considered the kinetic and thermal energy [2,3,7,8]. However, the existing framework is incomplete and provides limited insight into the exchange of mechanical energy among different forms or between fluid motions of different scales. In particular, the nature of the turbulent energy cascade in RBC is still not fully understood [3] and improved models are needed.Convection is caused by the generation of mechanical energy in the form of available potential energy (APE) by boundary buoyancy fluxes. APE is a subset of the total gravitational potential energy (GPE) and is the form essential for motions [9][10][11]. A complete mechanical energy framework has been recently developed for the case of horizontal convection forced by differential heating at one horizontal boundary [12,13] and recently extended to RBC [14]. In RBC there is a release of APE from thermal boundary layers adjacent to the top and bottom boundaries, driving flow at various scales, while complex feedbacks further distribute the potential and kinetic energy among the different scales or, through mixing, to the background potential energy. The role of APE in RBC was recognized in quantifying the overall rate of irreversible mixing [14]. Here we show that an account of GPE, its partition into available and background forms, and its links to kinetic energy at various scales are essential in a full understanding of the turbulent energy cascade and the relative roles of the boundary layer and the interior.

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“…Their theory fits many experimental data sets. 11 They predict a transition to an "ultimate" regime similar to Kraichnan's for Ra 10 14 and argue that their log correction would yield an effective scaling 12 of about Nu ∼ Ra 0.38 in the range 10 12 < Ra < 10 15 . Some experimental results show transition to an ultimate regime [13][14][15][16] while others do not.…”

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confidence: 86%

Heat transport by coherent Rayleigh-Bénard convection

2015

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Steady but generally unstable solutions of the 2D Boussinesq equations are obtained for no-slip boundary conditions and Prandtl number 7. The primary solution that bifurcates from the conduction state at Rayleigh number Ra ≈ 1708 has been calculated up to Ra ≈ 5.10 6 and its Nusselt number is N u ∼ 0.143 Ra 0.28 with a delicate spiral structure in the temperature field. Another solution that maximizes N u over the horizontal wavenumber has been calculated up to Ra = 10 9 and scales as N u ∼ 0.115 Ra 0.31 for 10 7 < Ra ≤ 10 9 , quite similar to 3D turbulent data that show N u ∼ 0.105 Ra 0.31 in that range. The optimum solution is a simple yet multi-scale coherent solution whose horizontal wavenumber scales as 0.133 Ra 0.217 . That solution is unstable to larger scale perturbations and in particular to mean shear flows, yet it appears to be relevant as a backbone for turbulent solutions, possibly setting the scale, strength and spacing of elemental plumes.

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On the triggering of the Ultimate Regime of convection

Cited by 118 publications

References 42 publications

New perspectives in turbulent Rayleigh-Bénard convection

New perspectives in turbulent Rayleigh-Bénard convection

Completing the Mechanical Energy Pathways in Turbulent Rayleigh-Bénard Convection

Heat transport by coherent Rayleigh-Bénard convection

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