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Dynamics of turbulent energy and dissipation in channel flow

Published online by Cambridge University Press:  26 September 2024

Le Yin Open the ORCID record for Le Yin [Opens in a new window] ,
Yongyun Hwang Open the ORCID record for Yongyun Hwang [Opens in a new window]  and
John Christos Vassilicos Open the ORCID record for John Christos Vassilicos [Opens in a new window]
Le Yin*
Affiliation:
UMR 9014 – LMFL – Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille, F-59000 Lille, France
Yongyun Hwang
Affiliation:
Department of Aeronautics, Imperial College London, South Kensington, London SW7 2AZ, UK
John Christos Vassilicos
Affiliation:
UMR 9014 – LMFL – Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille, F-59000 Lille, France
*
†Email address for correspondence: [email protected]
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Abstract

The dynamics of turbulent kinetic energy (TKE), turbulence dissipation rate (TDR) and turbulence production rate (TPR) are explored in fully developed turbulent channel flow using direct numerical simulations up to $\textit {Re}_\tau \approx 2000$ with minimal computational box for large-scale structures. Time correlation analysis based on volume-averaged TKE and TDR shows a well-defined average time lag, as in periodic/homogeneous turbulence, which, unlike periodic/homogeneous turbulence, appears to be Reynolds-number-dependent. On the basis of a spatio-temporal correlation analysis, we show that plane-averaged TKE fluctuations in the near-equilibrium region are transported towards both the core and near-wall regions, and are positively correlated with plane-averaged TDR fluctuations there with combined wall-distance and time lags. In the path towards the core region, the wall-distance lag is very close to the time lag multiplied by the friction velocity. The path towards the near-wall region has a wide spread of time lags, which increases with Reynolds number. The spatio-temporal correlation paths both towards the core and towards the wall are reproduced when the reference plane TKE is conditionally averaged on either ejections or sweeps, and are in fact stronger in correlation values in the case of ejections, which are better organised than sweeps. While volume-averaged TPR evidently precedes volume-averaged TKE, a more complex picture of non-local space–time correlations between reference plane TKE and TPR is revealed. A mechanistic model is proposed to elucidate these correlations between TKE and TPR through the interaction between the mean shear and the Reynolds shear stress.

JFM classification

Turbulent Flows: Turbulence theory Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 996 , 10 October 2024 , A12
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Apostolidis, A., Laval, J.-P. & Vassilicos, J.C. 2022 Scalings of turbulence dissipation in space and time for turbulent channel flow. J. Fluid Mech. 946, A41.CrossRefGoogle Scholar
Bewley, T. 2014 Numerical Renaissance: Simulation, Optimization, and Control. Renaissance Press.Google Scholar
Cheng, C., Shyy, W. & Fu, L. 2022 Streamwise inclination angle of wall-attached eddies in turbulent channel flows. J. Fluid Mech. 946, A49.CrossRefGoogle Scholar
Ciola, N., De Palma, P., Robinet, J.-C. & Cherubini, S. 2023 Nonlinear optimal perturbation of turbulent channel flow as a precursor of extreme events. J. Fluid Mech. 970, A6.CrossRefGoogle Scholar
Doohan, P., Bengana, Y., Yang, Q., Willis, A.P. & Hwang, Y. 2022 The state space and travelling-wave solutions in two-scale wall-bounded turbulence. J. Fluid Mech. 947, A41.CrossRefGoogle Scholar
Doohan, P., Willis, A.P. & Hwang, Y. 2019 Shear stress-driven flow: the state space of near-wall turbulence as $\textit {Re}_{\tau } \rightarrow \infty$. J. Fluid Mech. 874, 606–638.CrossRefGoogle Scholar
Doohan, P., Willis, A.P. & Hwang, Y. 2021 Minimal multi-scale dynamics of near-wall turbulence. J. Fluid Mech. 913, A8.CrossRefGoogle Scholar
Farano, M., Cherubini, S., Robinet, J.-C. & De Palma, P. 2017 Optimal bursts in turbulent channel flow. J. Fluid Mech. 817, 35–60.CrossRefGoogle Scholar
Flores, O. & Jiménez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22 (7), 071704.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence: The Legacy of A.N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Goto, S. & Vassilicos, J.C. 2015 Energy dissipation and flux laws for unsteady turbulence. Phys. Lett. A 379 (16), 1144–1148.CrossRefGoogle Scholar
Goto, S. & Vassilicos, J.C. 2016 Local equilibrium hypothesis and Taylor's dissipation law. Fluid Dyn. Res. 48 (2), 021402.CrossRefGoogle Scholar
Guala, M., Hommema, S.E. & Adrian, R.J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.CrossRefGoogle Scholar
Hamilton, J.M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to $\textit {Re}_\tau = 2003$. Phys. Fluids 18 (1), 011702.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647–664.Google ScholarPubMed
Hwang, Y. & Bengana, Y. 2016 Self-sustaining process of minimal attached eddies in turbulent channel flow. J. Fluid Mech. 795, 708–738.CrossRefGoogle Scholar
Hwang, Y. & Cossu, C. 2010 Self-sustained process at large scales in turbulent channel flow. Phys. Rev. Lett. 105, 044505.CrossRefGoogle ScholarPubMed
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.CrossRefGoogle Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59 (2), 308–323.CrossRefGoogle Scholar
Kim, K.C. & Adrian, R.J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.CrossRefGoogle Scholar
Kline, S.J., Reynolds, W.C., Schraub, F.A. & Runstadler, P.W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30 (4), 741–773.CrossRefGoogle Scholar
Kwon, Y.S., Philip, J., de Silva, C.M., Hutchins, N. & Monty, J.P. 2014 The quiescent core of turbulent channel flow. J. Fluid Mech. 751, 228–254.CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2015 Direct numerical simulation of turbulent channel flow up to $\textit {Re}_\tau \approx 5200$. J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Lozano-Durán, A. & Jiménez, J. 2014 a Effect of the computational domain on direct simulations of turbulent channels up to $\textit {Re}_\tau = 4200$. Phys. Fluids 26 (1), 011702.CrossRefGoogle Scholar
Lozano-Durán, A. & Jiménez, J. 2014 b Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades. J. Fluid Mech. 759, 432–471.CrossRefGoogle Scholar
Lu, S.S. & Willmarth, W.W. 1973 Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60 (3), 481–511.CrossRefGoogle Scholar
Marusic, I. & Heuer, W.D.C. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99, 114504.CrossRefGoogle ScholarPubMed
Pirozzoli, S. 2023 Searching for the log law in open channel flow. J. Fluid Mech. 971, A15.CrossRefGoogle Scholar
Sagaut, P. & Cambon, C. 2008 Homogeneous Turbulence Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Townsend, A.A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11 (1), 97–120.CrossRefGoogle Scholar
Vassilicos, J.C. 2015 Dissipation in turbulent flows. Annu. Rev. Fluid Mech. 47 (1), 95–114.CrossRefGoogle Scholar
Vassilicos, J.C. & Laval, J.-P. 2024 Scale-by-scale non-equilibrium in turbulent flows. In Coarse Graining Turbulence: Modeling and Data-Driven Approaches and their Applications (ed. Grinstein, F.F., Pereira, F.S. & Germano, M.). Cambridge University Press.Google Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883–900.CrossRefGoogle Scholar
Wallace, J.M., Eckelmann, H. & Brodkey, R.S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 54 (1), 39–48.CrossRefGoogle Scholar
Willmarth, W.W. & Lu, S.S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55 (1), 65–92.CrossRefGoogle Scholar
Yao, J., Chen, X. & Hussain, F. 2022 Direct numerical simulation of turbulent open channel flows at moderately high Reynolds numbers. J. Fluid Mech. 953, A19.CrossRefGoogle Scholar