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Universality of the energy-containing structures in wall-bounded turbulence

  • Charitha M. de Silva (a1), Dominik Krug (a1), Detlef Lohse (a2) (a3) and Ivan Marusic (a1)

The scaling behaviour of the longitudinal velocity structure functions $\langle (\unicode[STIX]{x1D6E5}_{r}u)^{2p}\rangle ^{1/p}$ (where $2p$ represents the order) is studied for various wall-bounded turbulent flows. It has been known that for very large Reynolds numbers within the logarithmic region, the structure functions can be described by $\langle (\unicode[STIX]{x1D6E5}_{r}u)^{2p}\rangle ^{1/p}/U_{\unicode[STIX]{x1D70F}}^{2}\approx D_{p}\ln (r/z)+E_{p}$ (where $r$ is the longitudinal distance, $z$ the distance from the wall, $U_{\unicode[STIX]{x1D70F}}$ the friction velocity and $D_{p}$ , $E_{p}$ are constants) in accordance with Townsend’s attached eddy hypothesis. Here we show that the ratios $D_{p}/D_{1}$ extracted from plots between structure functions – in the spirit of the extended self-similarity hypothesis – have further reaching universality for the energy containing range of scales. Specifically, we confirm that this description is universal across wall-bounded flows with different flow geometries, and also for both the longitudinal and transversal structure functions, where previously the scaling has been either difficult to discern or differences have been reported when examining the direct representation of $\langle (\unicode[STIX]{x1D6E5}_{r}u)^{2p}\rangle ^{1/p}$ . In addition, we present evidence of this universality at much lower Reynolds numbers, which opens up avenues to examine structure functions that are not readily available from high Reynolds number databases.

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J. C. del Alamo , J. Jiménez , P. Zandonade  & R. D. Moser 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135144.

A. Arneodo , C. Baudet , F. Belin , R. Benzi , B. Castaing , B. Chabaud , R. Chavarria , S. Ciliberto , R. Camussi , F. Chilla 1996 Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5000, using extended self-similarity. Europhys. Lett. 34, 411.

D. Chung , I. Marusic , J. P. Monty , M. Vallikivi  & A. J. Smits 2015 On the universality of inertial energy in the log layer of turbulent boundary layer and pipe flows. Exp. Fluids 56 (7), 110.

D. Chung  & B. J. McKeon 2010 Large-eddy simulation of large-scale structures in long channel flow. J. Fluid Mech. 661, 341364.

P. A. Davidson , T. B. Nickels  & P.-Å. Krogstad 2006 The logarithmic structure function law in wall-layer turbulence. J. Fluid Mech. 550, 5160.

D. J. C. Dennis  & T. B. Nickels 2008 On the limitations of Taylor’s hypothesis in constructing long structures in a turbulent boundary layer. J. Fluid Mech. 614, 197206.

U. Frisch 1995 Turbulence: The Legacy of AN Kolmogorov. Cambridge University Press.

S. Grossmann , D. Lohse  & A. Reeh 1997b Different intermittency for longitudinal and transversal turbulent fluctuations. Phys. Fluids 9, 38173825.

N. Hutchins , T. B. Nickels , I. Marusic  & M. S. Chong 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103136.

B. Jacob , L. Biferale , G. Iuso  & C. M. Casciola 2004 Anisotropic fluctuations in turbulent shear flows. Phys. Fluids 16 (11), 41354142.

J. Jiménez 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 2745.

G. J. Kunkel  & I. Marusic 2006 Study of the near-wall-turbulent region of the high-Reynolds number boundary layer using an atmospheric flow. J. Fluid Mech. 548, 375402.

C. Meneveau  & K. R. Sreenivasan 1987 Simple multifractal cascade model for fully developed turbulence. Phys. Rev. Lett. 59 (13), 1424.

H. C. H. Ng , J. P. Monty , N. Hutchins , M. S. Chong  & I. Marusic 2011 Comparison of turbulent channel and pipe flows with varying Reynolds number. Exp. Fluids 51 (5), 12611281.

T. B. Nickels , I. Marusic , S. Hafez  & M. S. Chong 2005 Evidence of the k -1 law in a high-Reynolds-number Turbulent Boundary Layer. Phys. Rev. Lett. 95 (7), 074501.

A. E. Perry , S. M. Henbest  & M. Chong 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163199.

S. B. Pope 2000 Turbulent Flows. Cambridge University Press.

Z. S. She  & E. Leveque 1994 Universal scaling law in fully developed turbulence. Phys. Rev. Lett. 72, 1424.

J. A. Sillero , J. Jiménez  & R. D. Moser 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to 𝛿+ = 2000. Phys. Fluids 25 (10), 105102.

C. M. de Silva , I. Marusic , J. D. Woodcock  & C. Meneveau 2015 Scaling of second-and higher-order structure functions in turbulent boundary layers. J. Fluid Mech. 769, 654686.

A. J. Smits , B. J. McKeon  & I. Marusic 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353375.

W. van de Water  & J. A. Herweijer 1999 High-order structure functions of turbulence. J. Fluid Mech. 387, 337.

X. I. A. Yang , I. Marusic  & C. Meneveau 2016a Moment generating functions and scaling laws in the inertial layer of turbulent wall-bounded flows. J. Fluid Mech. 791, R2.

X. I. A. Yang , C. Meneveau , I. Marusic  & L. Biferale 2016b Extended self-similarity in moment-generating-functions in wall-bounded turbulence at high Reynolds number. Phys. Rev. Fluids 1 (4), 044405.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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