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

2018/04/06 by Xiaojue Zhu, Varghese Mathai, Richard J. A. M. Stevens +2 · 2 citations
Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Boundary (topology) #Combustion and flame dynamics #Convection #Fluid Dynamics and Turbulent Flows #Geometry #Logarithm #Mathematical analysis #Mathematics #Mechanics #Natural convection #Nusselt number #Physics #Plant Water Relations and Carbon Dynamics #Prandtl number #Rayleigh number #Reynolds number #Scaling #Thermodynamics #Turbulence #Work (physics) #physics.flu-dyn

paper · pdf · doi:10.1103/physrevlett.120.144502

published as Phys. Rev. Lett. 120, 144502 (2018) · 6 pages, 4figures

openalex publication_date 2018/04/06 · arxiv created 2018/04/11 · arxiv updated 2018/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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)PFLDAS0031-917110.1063/1.1706533]. 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∼Ra^1/3 [Proc. R. Soc. A 225, 196 (1954)PRLAAZ1364-502110.1098/rspa.1954.0197]. 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∼Ra^0.38, corresponding to the effective scaling in the ultimate regime.

Citations

• Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection
• Turbulent Thermal Convection at Arbitrary Prandtl Number
• Logarithmic temperature profiles in the ultimate regime of thermal convection
• Small-Scale Properties of Turbulent Rayleigh-Bénard Convection

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