Transition to the Ultimate Regime in Two-Dimensional Rayleigh-Bénard Convection

Xiaojue Zhu (Corresponding Author), Varghese Mathai, Richard J.A.M. Stevens, Roberto Verzicco, Detlef Lohse (Corresponding Author)

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Abstract

The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue in thermal convection, since the seminal work by Kraichnan [Phys. Fluids 5, 1374 (1962)]. Yet, when this transition takes place and how the local flow induces it is not fully understood. Here, by performing two-dimensional simulations of Rayleigh-Bénard turbulence covering six decades in Rayleigh number Ra up to 1014 for Prandtl number Pr=1, for the first time in numerical simulations we find the transition to the ultimate regime, namely, at Ra∗=1013. We reveal how the emission of thermal plumes enhances the global heat transport, leading to a steeper increase of the Nusselt number than the classical Malkus scaling Nu∼Ra1/3 [Proc. R. Soc. A 225, 196 (1954)]. Beyond the transition, the mean velocity profiles are logarithmic throughout, indicating turbulent boundary layers. In contrast, the temperature profiles are only locally logarithmic, namely, within the regions where plumes are emitted, and where the local Nusselt number has an effective scaling Nu∼Ra0.38, corresponding to the effective scaling in the ultimate regime.
Original languageEnglish
Article number144502
JournalPhysical review letters
Volume120
Issue number14
DOIs
Publication statusPublished - 6 Apr 2018

Cite this

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title = "Transition to the Ultimate Regime in Two-Dimensional Rayleigh-B{\'e}nard Convection",
abstract = "The possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue in thermal convection, since the seminal work by Kraichnan [Phys. Fluids 5, 1374 (1962)]. Yet, when this transition takes place and how the local flow induces it is not fully understood. Here, by performing two-dimensional simulations of Rayleigh-B{\'e}nard turbulence covering six decades in Rayleigh number Ra up to 1014 for Prandtl number Pr=1, for the first time in numerical simulations we find the transition to the ultimate regime, namely, at Ra∗=1013. We reveal how the emission of thermal plumes enhances the global heat transport, leading to a steeper increase of the Nusselt number than the classical Malkus scaling Nu∼Ra1/3 [Proc. R. Soc. A 225, 196 (1954)]. Beyond the transition, the mean velocity profiles are logarithmic throughout, indicating turbulent boundary layers. In contrast, the temperature profiles are only locally logarithmic, namely, within the regions where plumes are emitted, and where the local Nusselt number has an effective scaling Nu∼Ra0.38, corresponding to the effective scaling in the ultimate regime.",
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Transition to the Ultimate Regime in Two-Dimensional Rayleigh-Bénard Convection. / Zhu, Xiaojue (Corresponding Author); Mathai, Varghese; Stevens, Richard J.A.M.; Verzicco, Roberto; Lohse, Detlef (Corresponding Author).

In: Physical review letters, Vol. 120, No. 14, 144502, 06.04.2018.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Lohse, Detlef

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