### 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 10^{14} for Prandtl number Pr = 1, for the first time in numerical simulations we find the transition to the ultimate regime, namely at Ra* = 10^{13}. 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. 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 ∼ Ra^{0.38}, 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 language | English |
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Title of host publication | Proceedings of the 21st Australasian Fluid Mechanics Conference, AFMC 2018 |

Editors | Timothy C.W. Lau, Richard M. Kelso |

Publisher | Australasian Fluid Mechanics Society |

ISBN (Electronic) | 9780646597843 |

Publication status | Published - 1 Jan 2018 |

Event | 21st Australasian Fluid Mechanics Conference, AFMC 2018 - Adelaide Convention Centre, Adelaide, Australia Duration: 10 Dec 2018 → 13 Dec 2018 Conference number: 21 |

### Publication series

Name | Proceedings of the 21st Australasian Fluid Mechanics Conference, AFMC 2018 |
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### Conference

Conference | 21st Australasian Fluid Mechanics Conference, AFMC 2018 |
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Abbreviated title | AFMC 2018 |

Country | Australia |

City | Adelaide |

Period | 10/12/18 → 13/12/18 |

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### Cite this

*Proceedings of the 21st Australasian Fluid Mechanics Conference, AFMC 2018*(Proceedings of the 21st Australasian Fluid Mechanics Conference, AFMC 2018). Australasian Fluid Mechanics Society.

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*Proceedings of the 21st Australasian Fluid Mechanics Conference, AFMC 2018.*Proceedings of the 21st Australasian Fluid Mechanics Conference, AFMC 2018, Australasian Fluid Mechanics Society, 21st Australasian Fluid Mechanics Conference, AFMC 2018, Adelaide, Australia, 10/12/18.

**Ultimate thermal turbulence and asymptotic ultimate turbulence induced by wall-roughness.** / Zhu, Xiaojue; Verschoof, Ruben A.; Bakhuis, Dennis; Mathai, Varghese; Huisman, Sander G.; Stevens, Richard J.A.M.; Verzicco, Roberto; Sun, Chao; Lohse, Detlef.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Ultimate thermal turbulence and asymptotic ultimate turbulence induced by wall-roughness

AU - Zhu, Xiaojue

AU - Verschoof, Ruben A.

AU - Bakhuis, Dennis

AU - Mathai, Varghese

AU - Huisman, Sander G.

AU - Stevens, Richard J.A.M.

AU - Verzicco, Roberto

AU - Sun, Chao

AU - Lohse, Detlef

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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].

AB - 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].

UR - http://www.scopus.com/inward/record.url?scp=85075193841&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85075193841

T3 - Proceedings of the 21st Australasian Fluid Mechanics Conference, AFMC 2018

BT - Proceedings of the 21st Australasian Fluid Mechanics Conference, AFMC 2018

A2 - Lau, Timothy C.W.

A2 - Kelso, Richard M.

PB - Australasian Fluid Mechanics Society

ER -