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Self-similarity of wall-attached turbulence in boundary layers

  • Woutijn J. Baars (a1), Nicholas Hutchins (a1) and Ivan Marusic (a1)


An assessment of the turbulent boundary layer flow structure, which is coherent with the near-wall region, is carried out through a spectral coherence analysis. This spectral method is applied to datasets comprising synchronized two-point streamwise velocity signals at a near-wall reference position and a range of wall-normal positions spanning a Reynolds-number range $Re_{\unicode[STIX]{x1D70F}}\sim O(10^{3}){-}O(10^{6})$ . Within each dataset, a self-similar structure is identified from the coherence between the turbulence in the logarithmic region and at the near-wall reference position. This self-similarity is described by a streamwise/wall-normal aspect ratio of $\unicode[STIX]{x1D706}_{x}/z\approx 14$ , where $\unicode[STIX]{x1D706}_{x}$ and $z$ are the streamwise wavelength and wall-normal distance respectively.


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Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 154.
Agostini, L. & Leschziner, M. 2017 Spectral analysis of near-wall turbulence in channel flow at Re 𝜏 = 4200 with emphasis on the attached-eddy hypothesis. Phys. Rev. Fluids 2, 014603.
del Álamo, J. C. & Jiménez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205213.
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135144.
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329358.
Baars, W. J., Hutchins, N. & Marusic, I. 2016 Spectral stochastic estimation of high-Reynolds-number wall-bounded turbulence for a refined inner–outer interaction model. Phys. Rev. Fluids 1, 054406.
Baars, W. J., Hutchins, N. & Marusic, I. 2017 Reynolds number trend of hierarchies and scale interactions in turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 375, 20160077.
Bullock, K. J., Cooper, R. E. & Abernathy, F. H. 1978 Structural similarity in radial correlations and spectra of longitudinal velocity fluctuations in pipe flow. J. Fluid Mech. 88, 585608.
Davenport, A. G. 1961 The spectrum of horizontal gustiness near the ground in high winds. Q. J. R. Meteorol. Soc. 87 (372), 194211.
Davidson, P. A. & Krogstad, P.-Å. 2009 A simple model for the streamwise fluctuations in the log-law region of a boundary layer. Phys. Fluids 21, 055105.
Davidson, P. A., Nickels, T. B. & Krogstad, P.-Å. 2006 The logarithmic structure function law in wall-layer turbulence. J. Fluid Mech. 550, 5160.
Hellström, L. H. O., Marusic, I. & Smits, A. J. 2016 Self-similarity of the large-scale motions in turbulent pipe flow. J. Fluid Mech. 792, R1.
Hutchins, N., Chauhan, K., Marusic, I. & Klewicki, J. 2012 Towards reconciling the large-scale structure of turbulent boundary layers in the atmosphere and laboratory. Boundary-Layer Meteorol. 145, 273306.
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering structures in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.
Hutchins, N., Monty, J. P., Ganapathisubramani, B., Ng, H. C. H. & Marusic, I. 2011 Three-dimensional conditional structure of a high-Reynolds-number turbulent boundary layer. J. Fluid Mech. 673, 255285.
Hwang, Y. 2015 Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech. 767, 254289.
Jiménez, J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 2745.
Jones, M. B., Marusic, I. & Perry, A. E. 2001 Evolution and structure of sink-flow turbulent boundary layers. J. Fluid Mech. 428, 127.
Klewicki, J., Fife, P. & Wei, T. 2009 On the logarithmic mean profile. J. Fluid Mech. 638, 7393.
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 = 5200. J. Fluid Mech. 774, 395415.
Lozano-Durán, A., Flores, O. & Jiménez, J. 2012 The three-dimensional structure of momentum transfer in turbulent channels. J. Fluid Mech. 694, 100130.
Marusic, I. & Heuer, W. D. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99, 114504.
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.
Marusic, I. & Perry, A. E. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support. J. Fluid Mech. 298, 389407.
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336382.
Morrison, W. R. B. & Kronauer, R. E. 1969 Structural similarity for fully developed turbulence in smooth tubes. J. Fluid Mech. 39, 117141.
Nickels, T. B., Marusic, I., Hafez, S. & Chong, M. S. 2005 Evidence of the k 1 -1 law in a high-Reynolds-number turbulent boundary layer. Phys. Rev. Lett. 95, 074501.
Örlü, R., Fiorini, T., Segalini, A., Bellani, G., Talamelli, A. & Alfredsson, P. H. 2017 Reynolds stress scaling in pipe flow turbulence – first results from CICLoPE. Phil. Trans. R. Soc. Lond. A 375, 20160187.
Perry, A. E. & Abell, C. J. 1975 Scaling laws for pipe-flow turbulence. J. Fluid Mech. 67, 257271.
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163199.
Rosenberg, B. J., Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2013 Turbulence spectra in smooth- and rough-wall pipe flow at extreme Reynolds numbers. J. Fluid Mech. 731, 4663.
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, 105102.
Talluru, K. M., Baidya, R., Hutchins, N. & Marusic, I. 2014 Amplitude modulation of all three velocity components in turbulent boundary layers. J. Fluid Mech. 746, R1.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Tutkun, M., George, W. K., Delville, J., Stanislas, M., Johansson, P. B. V., Foucaut, J.-M. & Coudert, S. 2009 Two-point correlations in high Reynolds number flat plate turbulent boundary layers. J. Turbul. 10, 123.
Vassilicos, J. C., Laval, J.-P., Foucaut, J.-M. & Stanislas, M. 2015 The streamwise turbulence intensity in the intermediate layer of turbulent pipe flow. J. Fluid Mech. 774, 324341.
Woodcock, J. D. & Marusic, I. 2015 The statistical behavior of attached eddies. Phys. Fluids 27, 015104.
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