Skip to main content
×
×
Home

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)
Abstract

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.

Copyright
Corresponding author
Email address for correspondence: desilvac@unimelb.edu.au
References
Hide All
del Alamo J. C., Jiménez J., Zandonade P. & Moser R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135144.
Arneodo A., Baudet C., Belin F., Benzi R., Castaing B., Chabaud B., Chavarria R., Ciliberto S., Camussi R., Chilla F. et al. 1996 Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5000, using extended self-similarity. Europhys. Lett. 34, 411.
Atkinson C., Buchmann N. A. & Soria J. 2014 An experimental investigation of turbulent convection velocities in a turbulent boundary layer. Flow Turbul. Combust. 94, 117.
Belin F., Tabeling P. & Willaime H. 1996 Exponents of the structure function in a low temperature helium experiment. Physica D 93, 52.
Benzi R., Ciliberto S., Baudet C. & Ruiz-Chavarria G. 1995 On the scaling of three-dimensional homogeneous and isotropic turbulence. Physica D 80, 385398.
Benzi R., Ciliberto S., Tripiccione R., Baudet C., Massaioli F. & Succi S. 1993 Extended self-similarity in turbulent flows. Phys. Rev. E 48, R29R32.
Chandran D., Baidya R., Monty J. & Marusic I. 2017 Two-dimensional energy spectra in high Reynolds number turbulent boundary layers. J. Fluid Mech. (to appear).
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), 110.
Chung D. & McKeon B. J. 2010 Large-eddy simulation of large-scale structures in long channel flow. J. Fluid Mech. 661, 341364.
Davidson P. A., Nickels T. B. & Krogstad P.-Å. 2006 The logarithmic structure function law in wall-layer turbulence. J. Fluid Mech. 550, 5160.
Del Alamo J. C. & Jiménez J. 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 526.
Dennis D. J. C. & Nickels T. B. 2008 On the limitations of Taylor’s hypothesis in constructing long structures in a turbulent boundary layer. J. Fluid Mech. 614, 197206.
Frisch U. 1995 Turbulence: The Legacy of AN Kolmogorov. Cambridge University Press.
Grossmann S., Lohse D. & Reeh A. 1997a Application of extended self similarity in turbulence. Phys. Rev. E 56, 5473.
Grossmann S., Lohse D. & Reeh A. 1997b Different intermittency for longitudinal and transversal turbulent fluctuations. Phys. Fluids 9, 38173825.
Huisman S. G., Lohse D. & Sun C. 2013 Statistics of turbulent fluctuations in counter-rotating Taylor–Couette flows. Phys. Rev. E 88, 063001.
Hutchins N., Nickels T. B., Marusic I. & Chong M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103136.
Jacob B., Biferale L., Iuso G. & Casciola C. M. 2004 Anisotropic fluctuations in turbulent shear flows. Phys. Fluids 16 (11), 41354142.
Jiménez J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 2745.
Kunkel G. J. & Marusic I. 2006 Study of the near-wall-turbulent region of the high-Reynolds number boundary layer using an atmospheric flow. J. Fluid Mech. 548, 375402.
Kurien S., Lvov V. S., Procaccia I. & Sreenivasan K. R. 2000 Scaling structure of the velocity statistics in atmospheric boundary layers. Phys. Rev. E 61 (1), 407.
Lee M. & Moser R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 = 5200. J. Fluid Mech. 774, 395415.
Marusic I., Monty J. P., Hultmark M. & Smits A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.
Meneveau C. & Marusic I. 2013 Generalized logarithmic law for high-order moments in turbulent boundary layers. J. Fluid Mech. 719, R1.
Meneveau C. & Sreenivasan K. R. 1987 Simple multifractal cascade model for fully developed turbulence. Phys. Rev. Lett. 59 (13), 1424.
Monty J. P., Hutchins N., Ng H. C. H., Marusic I. & Chong M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431442.
Ng H. C. H., Monty J. P., Hutchins N., Chong M. S. & Marusic I. 2011 Comparison of turbulent channel and pipe flows with varying Reynolds number. Exp. Fluids 51 (5), 12611281.
Nickels T. B., Marusic I., Hafez S. & Chong M. S. 2005 Evidence of the k -1 law in a high-Reynolds-number Turbulent Boundary Layer. Phys. Rev. Lett. 95 (7), 074501.
Perry A. E., Henbest S. M. & Chong M. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163199.
Pope S. B. 2000 Turbulent Flows. Cambridge University Press.
She Z. S. & Leveque E. 1994 Universal scaling law in fully developed turbulence. Phys. Rev. Lett. 72, 1424.
Sillero J. A., Jiménez J. & Moser R. D. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to 𝛿+ = 2000. Phys. Fluids 25 (10), 105102.
de Silva C. M., Marusic I., Woodcock J. D. & Meneveau C. 2015 Scaling of second-and higher-order structure functions in turbulent boundary layers. J. Fluid Mech. 769, 654686.
Smits A. J., McKeon B. J. & Marusic I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353375.
Townsend A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
van de Water W. & Herweijer J. A. 1999 High-order structure functions of turbulence. J. Fluid Mech. 387, 337.
Yang X. I. A., Marusic I. & Meneveau C. 2016a Moment generating functions and scaling laws in the inertial layer of turbulent wall-bounded flows. J. Fluid Mech. 791, R2.
Yang X. I. A., Meneveau C., Marusic I. & Biferale L. 2016b Extended self-similarity in moment-generating-functions in wall-bounded turbulence at high Reynolds number. Phys. Rev. Fluids 1 (4), 044405.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 9
Total number of PDF views: 330 *
Loading metrics...

Abstract views

Total abstract views: 427 *
Loading metrics...

* Views captured on Cambridge Core between 21st June 2017 - 22nd January 2018. This data will be updated every 24 hours.