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Scalings of scale-by-scale turbulence energy in non-homogeneous turbulence

Published online by Cambridge University Press:  10 March 2022

J.G. Chen Open the ORCID record for J.G. Chen [Opens in a new window]  and
J.C. Vassilicos Open the ORCID record for J.C. Vassilicos [Opens in a new window]
J.G. Chen
Affiliation:
Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille, UMR 9014 – LMFL – Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, F-59000 Lille, France
J.C. Vassilicos*
Affiliation:
Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille, UMR 9014 – LMFL – Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, F-59000 Lille, France
*
†Email address for correspondence: john-christos.vassilicos@centralelille.fr
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Abstract

A theory of non-homogeneous turbulence is developed and applied to boundary-free shear flows. The theory introduces assumptions of inner and outer similarity for the non-homogeneity of two-point statistics, and predicts power-law scalings of second-order structure functions that have some similarities with but also some differences from Kolmogorov scalings. These scalings arise as a consequence of these assumptions, of the general interscale and interspace energy balance, and of an inner–outer equivalence hypothesis for turbulence dissipation. They reduce to the usual Kolmogorov scalings in stationary homogeneous turbulence. Comparisons with structure function data from three qualitatively different turbulent wakes provide support for the theory's predictions but also raise new questions for future research.

JFM classification

Turbulent Flows: Turbulence theory Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 938 , 10 May 2022 , A7
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Afonso, M.M. & Sbragaglia, M. 2005 Inhomogeneous anisotropic passive scalars. J. Turbul. 6 (6), N10.CrossRefGoogle Scholar
Alam, M.M., Zhou, Y. & Wang, X.W. 2011 The wake of two side-by-side square cylinders. J. Fluid Mech. 669, 432–471.CrossRefGoogle Scholar
Alves Portela, F., Papadakis, G. & Vassilicos, J.C. 2017 The turbulence cascade in the near wake of a square prism. J. Fluid Mech. 825, 315–352.CrossRefGoogle Scholar
Alves Portela, F., Papadakis, G. & Vassilicos, J.C. 2020 The role of coherent structures and inhomogeneity in near-field interscale turbulent energy transfers. J. Fluid Mech. 896, A16.CrossRefGoogle Scholar
Batchelor, G.K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Cafiero, G. & Vassilicos, J.C. 2019 Non-equilibrium turbulence scalings and self-similarity in turbulent planar jets. Proc. R. Soc. Lond. A 475 (2225), 20190038.Google ScholarPubMed
Chen, J.G., Cuvier, C., Foucaut, J.-M., Ostovan, Y. & Vassilicos, J.C. 2021 A turbulence dissipation inhomogeneity scaling in the wake of two side-by-side square prisms. J. Fluid Mech. 924, A4.CrossRefGoogle Scholar
Chongsiripinyo, K. & Sarkar, S. 2020 Decay of turbulent wakes behind a disk in homogeneous and stratified fluids. J. Fluid Mech. 885, A31.CrossRefGoogle Scholar
Dairay, T., Obligado, M. & Vassilicos, J.C. 2015 Non-equilibrium scaling laws in axisymmetric turbulent wakes. J. Fluid Mech. 781, 166–195.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence: the Legacy of A.N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
George, W.K. & Hussein, H.J. 1991 Locally axisymmetric turbulence. J. Fluid Mech. 233, 1–23.CrossRefGoogle Scholar
Gomes-Fernandes, R., Ganapathisubramani, B. & Vassilicos, J.C. 2014 Evolution of the velocity-gradient tensor in a spatially developing turbulent flow. J. Fluid Mech. 756, 252–292.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 a Local equilibrium hypothesis and Taylor's dissipation law. Fluid Dyn. Res. 48 (2), 021402.CrossRefGoogle Scholar
Goto, S. & Vassilicos, J.C. 2016 b Unsteady turbulence cascades. Phys. Rev. E 94 (5), 053108.CrossRefGoogle ScholarPubMed
Hill, R.J. 2001 Equations relating structure functions of all orders. J. Fluid Mech. 434, 379–388.CrossRefGoogle Scholar
Hill, R.J. 2002 Exact second-order structure-function relationships. J. Fluid Mech. 468, 317–326.CrossRefGoogle Scholar
Jurčišinová, E. & Jurčišin, M. 2008 Anomalous scaling of a passive scalar advected by a turbulent velocity field with finite correlation time and uniaxial small-scale anisotropy. Phys. Rev. E 77, 016306.CrossRefGoogle ScholarPubMed
Kaneda, Y. 2020 Linear response theory of turbulence. J. Stat. Mech. Theory Exp. 2020 (3), 034006.CrossRefGoogle Scholar
Klingenberg, D., Oberlack, M. & Pluemacher, D. 2020 Symmetries and turbulence modeling. Phys. Fluids 32 (2), 025108.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 a Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16–18.Google Scholar
Kolmogorov, A.N. 1941 b The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305.Google Scholar
Kraichnan, R.H. 1974 On Kolmogorov's inertial-range theories. J. Fluid Mech. 62 (2), 305–330.CrossRefGoogle Scholar
Lefeuvre, N., Thiesset, F., Djenidi, L. & Antonia, R.A. 2014 Statistics of the turbulent kinetic energy dissipation rate and its surrogates in a square cylinder wake flow. Phys. Fluids 26 (9), 095104.CrossRefGoogle Scholar
Mathieu, J. & Scott, J. 2000 An Introduction to Turbulent Flow. Cambridge University Press.CrossRefGoogle Scholar
Obligado, M., Dairay, T. & Vassilicos, J.C. 2016 Nonequilibrium scalings of turbulent wakes. Phys. Rev. Fluids 1 (4), 044409.CrossRefGoogle Scholar
Obukhov, A.M. 1941 On the distribution of energy in the spectrum of turbulent flow. Bull. Acad. Sci. USSR Ser. Geophys. 5, 453–466.Google Scholar
Ortiz-Tarin, J.L., Nidhan, S. & Sarkar, S. 2021 High-Reynolds-number wake of a slender body. J. Fluid Mech. 918, A30.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Sagaut, P. & Cambon, C. 2018 Homogeneous Turbulence Dynamics. Springer.CrossRefGoogle Scholar
Sumner, D., Wong, S.S.T., Price, S.J. & Paidoussis, M.P. 1999 Fluid behaviour of side-by-side circular cylinders in steady cross-flow. J. Fluids Struct. 13 (3), 309–338.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J.L. 1972 A First Course in Turbulence. MIT.CrossRefGoogle Scholar
Valente, P.C. & Vassilicos, J.C. 2015 The energy cascade in grid-generated non-equilibrium decaying turbulence. Phys. Fluids 27 (4), 045103.CrossRefGoogle Scholar
Vassilicos, J.C. 2015 Dissipation in turbulent flows. Annu. Rev. Fluid Mech. 47, 95–114.CrossRefGoogle Scholar
Zhou, Y., Nagata, K., Sakai, Y. & Watanabe, T. 2019 Extreme events and non-Kolmogorov $-5/3$ spectra in turbulent flows behind two side-by-side square cylinders. J. Fluid Mech. 874, 677–698.CrossRefGoogle Scholar
Zhou, Y. & Vassilicos, J.C. 2020 Energy cascade at the turbulent/nonturbulent interface. Phys. Rev. Fluids 5 (6), 064604.CrossRefGoogle Scholar