# Wall roughness induces asymptotic ultimate turbulence

## Abstract

Turbulence governs the transport of heat, mass and momentum on multiple scales. In real-world applications, wall-bounded turbulence typically involves surfaces that are rough; however, characterizing and understanding the effects of wall roughness on turbulence remains a challenge. Here, by combining extensive experiments and numerical simulations, we examine the paradigmatic Taylor–Couette system, which describes the closed flow between two independently rotating coaxial cylinders. We show how wall roughness greatly enhances the overall transport properties and the corresponding scaling exponents associated with wall-bounded turbulence. We reveal that if only one of the walls is rough, 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 eliminated, giving rise to asymptotic ultimate turbulence—the upper limit of transport—the existence of which was predicted more than 50 years ago. In this limit, the scaling laws can be extrapolated to arbitrarily large Reynolds numbers.

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## Acknowledgements

We gratefully acknowledge V. Mathai for insightful discussions. We thank G. W. Bruggert and M. Bos, as well as G. Mentink and R. Nauta, for their technical support and D.P.M. van Gils and R. Ezeta for various discussions and help with the experiments. The work is financially supported by NWO-I, NWO-TTW, the Netherlands Center for Multiscale Catalytic Energy Conversion (MCEC), and a VIDI grant (No. 13477), all sponsored by the Netherlands Organisation for Scientific Research (NWO). C.S. acknowledges the financial support from Natural Science Foundation of China under Grant No. 11672156. Part of the simulations were carried out on the Dutch national e-infrastructure with the support of SURF Cooperative. We also acknowledge PRACE for awarding us access to Marconi at CINECA, Italy under PRACE project number 2016143351 and DECI resource ARCHER UK National Supercomputing Service with the support from PRACE under project 13DECI0246.

## Author information

Authors

### Contributions

X.Z., S.G.H., R.A.V., R.V., C.S. and D.L. conceived the ideas. X.Z. performed the numerical simulations. R.A.V. and D.B. performed the measurements. X.Z. and R.A.V. analysed the data. X.Z., R.A.V. and D.L. wrote the paper. R.V., C.S. and D.L. supervised the project. All authors discussed the physics and proofread the paper.

### Corresponding authors

Correspondence to Chao Sun or Detlef Lohse.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

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## Supplementary information

### Supplementary Figures

Supplementary Figures S1–S5

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Zhu, X., Verschoof, R.A., Bakhuis, D. et al. Wall roughness induces asymptotic ultimate turbulence. Nature Phys 14, 417–423 (2018). https://doi.org/10.1038/s41567-017-0026-3

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