Ultimate thermal turbulence and asymptotic ultimate turbulence induced by wall-roughness

Xiaojue Zhu, Ruben A. Verschoof, Dennis Bakhuis, Varghese Mathai, Sander G. Huisman, Richard J.A.M. Stevens, Roberto Verzicco, Chao Sun, Detlef Lohse

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Abstract

Turbulence is omnipresent in Nature and technology, governing the transport of heat, mass, and momentum on multiple scales. One of the paradigmatic turbulent flows is Rayleigh-Bénard convection, i.e., a flow heated from below and cooled from above. Here, the possible transition to the so-called ultimate regime, wherein both the bulk and the boundary layers are turbulent, has been an outstanding issue, 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. 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. London 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. For real-world applications of wall-bounded turbulence, the underlying surfaces are virtually always rough; yet characterizing and understanding the effects of wall roughness for turbulence remains an elusive challenge. By combining extensive experiments and numerical simulations, here, taking as 2nd example the paradigmatic Taylor-Couette system (the closed flow between two independently rotating coaxial cylinders), we uncover the mechanism that causes the considerable enhancement of the overall transport properties by wall roughness. If only one of the walls is rough, we reveal that the bulk velocity is slaved to the rough side, due to the much stronger coupling to that wall by the detaching flow structures. If both walls are rough, the viscosity dependence is thoroughly eliminated and we thus achieve what we call asymptotic ultimate turbulence, i.e. the upper limit of transport, in which the scalings laws can be extrapolated to arbitrarily large Reynolds numbers. This Proceeding contribution summarizes and reproduces the main results of our recent references [56, 57].

Original languageEnglish
Title of host publicationProceedings of the 21st Australasian Fluid Mechanics Conference, AFMC 2018
EditorsTimothy C.W. Lau, Richard M. Kelso
PublisherAustralasian Fluid Mechanics Society
ISBN (Electronic)9780646597843
Publication statusPublished - 1 Jan 2018
Event21st Australasian Fluid Mechanics Conference, AFMC 2018 - Adelaide Convention Centre, Adelaide, Australia
Duration: 10 Dec 201813 Dec 2018
Conference number: 21

Publication series

NameProceedings of the 21st Australasian Fluid Mechanics Conference, AFMC 2018

Conference

Conference21st Australasian Fluid Mechanics Conference, AFMC 2018
Abbreviated titleAFMC 2018
CountryAustralia
CityAdelaide
Period10/12/1813/12/18

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Zhu, X., Verschoof, R. A., Bakhuis, D., Mathai, V., Huisman, S. G., Stevens, R. J. A. M., ... Lohse, D. (2018). Ultimate thermal turbulence and asymptotic ultimate turbulence induced by wall-roughness. In T. C. W. Lau, & R. M. Kelso (Eds.), Proceedings of the 21st Australasian Fluid Mechanics Conference, AFMC 2018 (Proceedings of the 21st Australasian Fluid Mechanics Conference, AFMC 2018). Australasian Fluid Mechanics Society.