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Reynolds stress scaling in the near-wall region of wall-bounded flows

Published online by Cambridge University Press:  14 September 2021

Alexander J. Smits Open the ORCID record for Alexander J. Smits [Opens in a new window] ,
Marcus Hultmark Open the ORCID record for Marcus Hultmark [Opens in a new window] ,
Myoungkyu Lee Open the ORCID record for Myoungkyu Lee [Opens in a new window] ,
Sergio Pirozzoli Open the ORCID record for Sergio Pirozzoli [Opens in a new window]  and
Xiaohua Wu Open the ORCID record for Xiaohua Wu [Opens in a new window]
Alexander J. Smits*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Marcus Hultmark
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Myoungkyu Lee
Affiliation:
Sandia National Laboratories, Livermore, CA 94551, USA
Sergio Pirozzoli
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma ‘La Sapienza’, 00184 Roma, Italy
Xiaohua Wu
Affiliation:
Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, ON K7K 7B4, Canada
*
†Email address for correspondence: [email protected]
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Abstract

A new scaling is derived that yields a Reynolds-number-independent profile for all components of the Reynolds stress in the near-wall region of wall-bounded flows, including channel, pipe and boundary layer flows. The scaling demonstrates the important role played by the wall shear stress fluctuations and how the large eddies determine the Reynolds number dependence of the near-wall turbulence behaviour.

JFM classification

Boundary Layers: Boundary layer structure Boundary Layers: Pipe flow boundary layer Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 926 , 10 November 2021 , A31
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Agostini, L. & Leschziner, M. 2016 On the validity of the quasi-steady-turbulence hypothesis in representing the effects of large scales on small scales in boundary layers. Phys. Fluids 28 (4), 045102.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M. 2018 The impact of footprints of large-scale outer structures on the near-wall layer in the presence of drag-reducing spanwise wall motion. Flow Turbul. Combust. 100 (4), 1037–1061.CrossRefGoogle Scholar
Bewley, T.R. & Protas, B. 2004 Skin friction and pressure: the ‘footprints’ of turbulence. Phys. D: Nonlinear Phenom. 196 (1–2), 28–44.CrossRefGoogle Scholar
Chen, X. & Sreenivasan, K.R. 2021 Reynolds number scaling of the peak turbulence intensity in wall flows. J. Fluid Mech. 908, R3.CrossRefGoogle Scholar
Chung, D., Marusic, I., Monty, J.P., Vallikivi, M. & Smits, A.J. 2015 On the universality of inertial energy in the log layer of turbulent boundary layer and pipe flows. Exp. Fluids 56 (7), 1–10.CrossRefGoogle Scholar
Cimarelli, A., De Angelis, E., Schlatter, P., Brethouwer, G., Talamelli, A. & Casciola, C.M. 2015 Sources and fluxes of scale energy in the overlap layer of wall turbulence. J. Fluid Mech. 771, 407–423.CrossRefGoogle Scholar
DeGraaff, D.B. & Eaton, J.K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Hultmark, M. & Smits, A.J. 2021 Scaling turbulence in the near-wall region. Preprint. arXiv:2103.01765.Google Scholar
Hultmark, M., Vallikivi, M., Bailey, S.C.C. & Smits, A.J. 2013 Logarithmic scaling of turbulence in smooth- and rough-wall pipe flow. J. Fluid Mech. 728, 376–395.CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2015 Direct numerical simulation of turbulent channel flow up to $Re_\tau \approx 5200$. J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2017 Role of large-scale motions in turbulent Poiseuille and Couette flows. In Proceedings of 10th Symposium on Turbulence and Shear Flow Phenomena, Chicago, USA, vol. 10, p. 9B-3.Google Scholar
Lee, M. & Moser, R.D. 2018 Extreme-scale motions in turbulent plane Couette flows. J. Fluid Mech. 842, 128–145.CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2019 Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number. J. Fluid Mech. 860, 886–938.CrossRefGoogle Scholar
Lozano-Durán, A. & Jiménez, J. 2014 Effect of the computational domain on direct simulations of turbulent channels up to $Re_\tau = 4200$. Phys. Fluids 26, 011702.CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329, 193–196.CrossRefGoogle ScholarPubMed
Mathis, R., Marusic, I., Chernyshenko, S.I. & Hutchins, N. 2013 Estimating wall-shear-stress fluctuations given an outer region input. J. Fluid Mech. 715, 163.CrossRefGoogle Scholar
McKeon, B.J., Li, J., Jiang, W., Morrison, J.F. & Smits, A.J. 2004 Further observations on the mean velocity distribution in fully developed pipe flow. J. Fluid Mech. 501, 135–147.CrossRefGoogle Scholar
Monkewitz, P.A. 2021 Asymptotics of stream-wise Reynolds stress in wall turbulence. Preprint. arXiv:2104.07322.Google Scholar
Orlandi, P., Bernardini, M. & Pirozzoli, S. 2015 Poiseuille and Couette flows in the transitional and fully turbulent regime. J. Fluid Mech. 770, 424.CrossRefGoogle Scholar
Örlü, R. & Schlatter, P. 2011 On the fluctuating wall-shear stress in zero pressure-gradient turbulent boundary layer flows. Phys. Fluids 23, 21704.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Orlandi, P. 2014 Turbulence statistics in Couette flow at high Reynolds number. J. Fluid Mech. 758, 327–343.CrossRefGoogle Scholar
Pirozzoli, S., Romero, J., Fatica, M., Verzicco, R. & Orlandi, P. 2021 One-point statistics for turbulent pipe flow up to $Re_{\tau} \approx 6000$. J. Fluid Mech. (submitted).CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Samie, M., Marusic, I., Hutchins, N., Fu, M.K., Fan, Y., Hultmark, M. & Smits, A.J. 2018 Fully resolved measurements of turbulent boundary layer flows up to $Re_\tau = 20$, 000. J. Fluid Mech. 851, 391–415.CrossRefGoogle Scholar
Sillero, J.A., Jiménez, J. & Moser, R.D. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to $\delta ^+ \approx 2000$. Phys. Fluids 25 (10), 105102.CrossRefGoogle Scholar
Sillero, J.A., Jiménez, J., Moser, R.D. & Malaya, N.P. 2011 Direct simulation of a zero-pressure-gradient turbulent boundary layer up to $Re_\theta = 6650$. J. Phys.: Conf. Ser. 318, 022023.Google Scholar
Smits, A.J. & Hultmark, M. 2021 Reynolds stress scaling in the near-wall region. Preprint. arXiv:2103.07341.Google Scholar
Townsend, A.A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Wu, X., Moin, P., Wallace, J.M., Skarda, J., Lozano-Durán, A. & Hickey, J.-P. 2017 Transitional–turbulent spots and turbulent–turbulent spots in boundary layers. Proc. Natl Acad. Sci. USA 114 (27), E5292–E5299.CrossRefGoogle ScholarPubMed
Yang, X.I.A. & Lozano-Durán, A. 2017 A multifractal model for the momentum transfer process in wall-bounded flows. J. Fluid Mech. 824, R2.CrossRefGoogle ScholarPubMed
Zagarola, M.V. & Smits, A.J. 1998 Mean-flow scaling of turbulent pipe flow. J. Fluid Mech. 373, 33–79.CrossRefGoogle Scholar