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Thermal forcing and ‘classical’ and ‘ultimate’ regimes of Rayleigh–Bénard convection

  • Charles R. Doering (a1)

Abstract

The fundamental challenge to characterize and quantify thermal transport in the strongly nonlinear regime of Rayleigh–Bénard convection – the buoyancy-driven flow of a horizontal layer of fluid heated from below – has perplexed the fluid dynamics community for decades. Rayleigh proposed controlling the temperature of thermally conducting boundaries in order to study the onset of convection, in which case vertical heat transport gauges the system response. Conflicting experimental results for ostensibly similar set-ups have confounded efforts to discriminate between two competing theories for how boundary layers and interior flows interact to determine transport through the convecting layer asymptotically far beyond onset. In a conceptually new approach, Bouillaut, Lepot, Aumaître and Gallet (J. Fluid Mech., vol. 861, 2019, R5) devised a procedure to radiatively heat a portion of the fluid domain bypassing rigid conductive boundaries and allowing for dissociation of thermal and viscous boundary layers. Their experiments reveal a new level of complexity in the problem suggesting that heat transport scaling predictions of both theories may be realized depending on details of the thermal forcing.

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Copyright

Corresponding author

Email address for correspondence: doering@umich.edu

References

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Batchelor, G. K. 1961 Considerations of convective instability from the viewpoint of physics. Discussion. In Aerodynamics Phenomena in Stellar Atmospheres, Proceedings of the 4th Symposium on Cosmical Gas Dynamics, August 18–30, 1960 (ed. Thomas, R. N.), pp. 385402. N. Zanichelli.
Borue, V. & Orszag, S. A. 1997 Turbulent convection driven by a constant temperature gradient. J. Sci. Comput. 12, 305351.
Bouillaut, V., Lepot, S., Aumaître, S. & Gallet, B. 2019 Transition to the ultimate regime in a radiatively driven convection experiment. J. Fluid Mech. 861, R5.10.1017/jfm.2018.972
Calzavarini, E., Doering, C. R., Gibbon, J. D., Lohse, D., Tanabe, A. & Toschi, F. 2006 Exponentially growing solutions in homogeneous Rayleigh–Bénard convection. Phys. Rev. E 73, 035301R.
Chavanne, X., Chillà, F., Castaing, H. B., Chabaud, B. & Chaussy, J. 1997 Observation of the ultimate regime in Rayleigh–Bénard convection. Phys. Rev. Lett. 79, 36483651.
Doering, C. R. & Constantin, P. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E 53, 59575981.
Fantuzzi, G. & Doering, C. R.2018 Bounds for convection between perfectly insulating boundaries driven by internal heat sources and sinks. Unpublished notes.
Goluskin, D. 2016 Internally Heated Convection and Rayleigh–Bénard Convection. Springer.
Howard, L. N. 1963 Heat transport by turbulent convection. J. Fluid Mech. 17, 405432.10.1017/S0022112063001427
Howard, L. N. 1964 Convection at high Rayleigh numbers. In Applied Mechanics, Proceedings of the 11th Congress of Applied Mechanics (ed. Görtler, H.), pp. 11091115. Springer.
Hurle, D. T. J., Jakeman, E. & Pike, E. R. 1967 On the solution of the Bénard problem with boundaries of finite conductivity. Proc. R. Soc. Lond. A 296, 469475.
Johnston, H. & Doering, C. R. 2009 Comparison of turbulent thermal convection between conditions of constant temperature and constant flux. Phys. Rev. Lett. 102, 064501.
Kraichnan, R. H. 1962 Turbulent thermal convection at arbitrary Prandtl number. Phys. Fluids 5, 13741389.10.1063/1.1706533
Lepot, S.2018 Radiatively driven convection: from the Rayleigh–Bénard regime to the ultimate regime. PhD thesis, Université Paris-Saclay.
Lepot, S., Aumaître, S. & Gallet, B. 2018 Radiative heating achieves the ultimate regime of thermal convection. Proc. Natl Acad. Sci. USA 115, 89378941.10.1073/pnas.1806823115
Lord Rayleigh 1916 On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side. Phil. Mag. 32, 529546.10.1080/14786441608635602
Malkus, W. V. R. 1954 The heat transport and spectrum of thermal turbulence. Proc. R. Soc. Lond. A 225, 196212.
Muite, B. K., Whitehead, J. P. & Doering, C. R.2017 Infinite Prandtl number two-dimensional non-uniformly internally heat driven convection on ${\mathcal{T}}^{2}$ . In Abstracts of the 22nd International Conference Mathematical Modelling & Analysis (http://inga.vgtu.lt/∼art/konf/first.php), May 30–June 2, 2017. Druskininkai, Lithuania.
Pearson, J. R. A. 1958 On convection cells induced by surface tension. J. Fluid Mech. 4, 489500.10.1017/S0022112058000616
Priestly, C. H. B. 1954 Convection from a large horizontal surface. Austral. J. Phys. 7, 176201.
Spiegel, E. A. 1963 A generalization of the mixing-length theory of thermal convection. Astrophys. J. 138, 216225.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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