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Spatial modulations of kinetic energy in the roughness sublayer

Published online by Cambridge University Press:  06 July 2018

Jérémy Basley Open the ORCID record for Jérémy Basley [Opens in a new window] ,
Laurent Perret  and
Romain Mathis Open the ORCID record for Romain Mathis [Opens in a new window]
Jérémy Basley*
Affiliation:
LHEEA, UMR 6598 CNRS Centrale Nantes, 44300 Nantes, France Department of Aeronautics, Imperial College London, Kensington, London SW7 2AZ, UK
Laurent Perret
Affiliation:
LHEEA, UMR 6598 CNRS Centrale Nantes, 44300 Nantes, France
Romain Mathis
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, 31400 Toulouse, France
*
†Email address for correspondence: [email protected]
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Abstract

High-Reynolds-number experiments are conducted in the roughness sublayer of a turbulent boundary layer developing over a cubical canopy. Stereoscopic particle image velocimetry is performed in a wall-parallel plane to evidence a high degree of spatial modulation of the small-scale turbulence around the footprint of large-scale motions, despite the suppression of the inner layer by the high roughness elements. Both Fourier and wavelets analyses show that the near-wall cycle observed in smooth-wall-bounded flows is severely disrupted by the canopy, whose wake in the roughness sublayer generates a new range of scales, closer to that of the outer-layer large-scale motions. This restricts significantly scale separation, hence a diagnostic method is developed to divide carefully and rationally the fluctuating velocity fields into large- and small-scale components. Our analysis across all turbulent kinetic energy terms sheds light on the spatial imprint of the modulation mechanism, revealing a very different signature on each velocity component. The roughness sublayer shows a preferential arrangement of the modulated scales similar to what is observed in the outer layer of smooth-wall-bounded flows – small-scale turbulence is enhanced near the front of high momentum regions and damped at the front of low momentum regions. More importantly, accessing spanwise correlations reveals that modulation intensifies the most along the flanks of the large-scale motions.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 850 , 10 September 2018 , pp. 584 - 610
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Copyright
© 2018 Cambridge University Press 

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References

Adrian, R. J., Christensen, K. T. & Liu, Z.-C. 2000a Analysis and interpretation of instantaneous turbulent velocity fields. Exp. Fluids 29, 275–290.Google Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000b Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.Google Scholar
Agostini, L. & Leschziner, M. A. 2014 On the influence of outer large-scale structures on near-wall turbulence in channel flow. Phys. Fluids 26, 075107.Google Scholar
Agostini, L., Leschziner, M. A. & Gaitonde, D. 2016 Skewness-induced asymmetric modulation of small-scale turbulence by large-scale structures. Phys. Fluids 28, 015110.Google Scholar
Ahn, J., Lee, J. H. & Sung, H. J. 2013 Statistics of the turbulent boundary layers over 3d cube-roughened walls. Intl J. Heat Fluid Flow 44, 394–402.Google Scholar
Anderson, W. 2016 Amplitude modulation of streamwise velocity fluctuations in the roughness sublayer: evidence from large-eddy simulations. J. Fluid Mech. 789, 567–588.Google Scholar
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.Google Scholar
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.Google Scholar
Baars, W. J., Talluru, K. M., Hutchins, N. & Marusic, I. 2015 Wavelet analysis of wall turbulence to study large-scale modulation of small scales. Exp. Fluids 56 (10), 188.Google Scholar
Bandyopadhyay, P. R. & Hussain, A. K. M. F. 1984 The coupling between scales in shear flows. Phys. Fluids 27 (9), 2221.Google Scholar
Barros, J. M. & Christensen, K. T. 2014 Observations of turbulent secondary flows in a rough-wall boundary layer. J. Fluid Mech. 748, R1.Google Scholar
Basley, J. & Perret, L. 2017 Signature of a cubical canopy on the spatial dynamics of an atmospheric boundary layer. In Progress in Turbulence VII – Proceedings of the Interdisciplinary Turbulence Initiative, pp. 205–210. Springer.Google Scholar
Blackman, K. & Perret, L. 2016 Non-linear interactions in a boundary layer developing over an array of cubes using stochastic estimation. Phys. Fluids 28, 095108.Google Scholar
Blackman, K., Perret, L., Calmet, I. & Rivet, C. 2017 Turbulent kinetic energy budget in the boundary layer developing over an urban-like rough wall using PIV. Phys. Fluids 29, 1–19.Google Scholar
Blackwelder, R. F. & Kovasznay, L. S. G. 1972 Time scales and correlations in a turbulent boundary layer. Phys. Fluids 15, 1545.Google Scholar
Brown, G. L. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20, 243–252.Google Scholar
Burrus, C., Gopinath, R. & Guo, H. 1998 Introduction to Wavelets and Wavelet Transform – A Primer. Prentice-Hall.Google Scholar
Castro, I. P., Cheng, H. & Reynolds, R. 2006 Turbulence over urban-type roughness: deductions from wind-tunnel measurements. Boundary-Layer Meteorol. 118, 109–131.Google Scholar
Castro, I. P., Segalini, A. & Alfredsson, P. H. 2013 Outer-layer turbulence intensities in smooth- and rough-wall boundary layers. J. Fluid Mech. 727, 119–131.Google Scholar
Cheng, H. & Castro, I. P. 2002 Near wall flow over urban-like roughness. Boundary-Layer Meteorol. 104, 229–259.Google Scholar
Cheng, H., Hayden, P. & Robins, A. G. 2007 Flow over cube arrays of different packing densities. J. Wind Engng Ind. Aerodyn. 95, 715–740.Google Scholar
Coceal, O., Dobre, A., Thomas, T. G. & Belcher, S. E. 2007 Structure of turbulent flow over regular arrays of cubical roughness. J. Fluid Mech. 589, 375–409.Google Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds number scaling of the flat plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.Google Scholar
Dennis, D. J. C. & Nickels, T. B. 2011a Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 1. Vortex packets. J. Fluid Mech. 673, 180–217.Google Scholar
Dennis, D. J. C. & Nickels, T. B. 2011b Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 2. Long structures. J. Fluid Mech. 673, 218–244.Google Scholar
Fiscaletti, D., Ganapathisubramani, B. & Elsinga, G. E. 2015 Amplitude and frequency modulation of the small scales in a jet. J. Fluid Mech. 772, 756–783.Google Scholar
Ganapathisubramani, B., Hutchins, N., Hambleton, W. T., Longmire, E. K. & Marusic, I. 2005 Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations. J. Fluid Mech. 524, 57–80.Google Scholar
Ganapathisubramani, B., Hutchins, N., Monty, J. P., Chung, D. & Marusic, I. 2012 Amplitude and frequency modulation in wall turbulence. J. Fluid Mech. 782, 1–31.Google Scholar
Guala, M., Metzger, M. & McKeon, B. J. 2011 Interactions within the turbulent boundary layer at high Reynolds number. J. Fluid Mech. 666, 573–604.Google Scholar
Hagishima, A., Tanimoto, J., Nagayama, K. & Meno, S. 2009 Aerodynamic parameters of regular arrays of rectangular blocks with various geometries. Boundary-Layer Meteorol. 132, 315–337.Google Scholar
Harun, Z., Monty, J. P., Mathis, R. & Marusic, I. 2013 Pressure gradient effects on the large-scale structure of turbulent layers. J. Fluid Mech. 715, 477–498.Google Scholar
Hunt, J. C. & Morrison, J. F. 2000 Eddy structure in turbulent boundary layers. Eur. J. Mech. (B/Fluids) 19 (5), 673–694.Google Scholar
Hutchins, N. & Marusic, I. 2007a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.Google Scholar
Hutchins, N. & Marusic, I. 2007b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365, 647–664.Google Scholar
Inagaki, A., Castillo, M. C. L., Yamashita, Y., Kanda, M. & Takimoto, H. 2012 Large-eddy simulation of coherent flow structures within a cubical canopy. Boundary-Layer Meteorol. 142, 207–222.Google Scholar
Inagaki, A. & Kanda, M. 2010 Organized structure of active turbulence over an array of cubes within the logarithmic layer of atmospheric flow. Boundary-Layer Meteorol. 135 (2), 209–228.Google Scholar
Kanda, M., Kanega, M. K., Kawai, T. K., Moriwaki, R. & Sugawara, H. 2007 Roughness lengths for momentum and heat derived from outdoor urban scale models. J. Appl. Meteorol. Climatol. 47, 1067–1073.Google Scholar
Kanda, M., Moriwaki, R. & Kasamatsu, F. 2004 Large eddy simulation of turbulent organized structure within and above explicitly resolved cubic arrays. Boundary-Layer Meteorol. 112, 343–368.Google Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417.Google Scholar
Lee, J. H., Sung, H. J. & Krogstad, P.-A. 2011 Direct numerical simulation of the turbulent boundary layer over a cube-roughened wall. J. Fluid Mech. 669, 1–35.Google Scholar
Leonardi, S. & Castro, I. P. 2010 Channel flow over large cube roughness: a direct numerical simulation study. J. Fluid Mech. 651, 1.Google Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329, 193–196.Google Scholar
Marusic, I., Monty, J., Hultmark, M. & Smits, A. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716 (R3), 1–11.Google Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.Google Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2011a A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows. J. Fluid Mech. 681, 537–566.Google Scholar
Mathis, R., Marusic, I., Hutchins, N. & Sreenivasan, K. R. 2011b The relationship between the velocity skewness and the amplitude modulation of the small scale by the large scale in turbulent boundary layers. Phys. Fluids 23 (12), 121702.Google Scholar
McKeon, B. J. 2017 The engine behind (wall) turbulence: perspectives on scale interactions. J. Fluid Mech. 817, P1.Google Scholar
Mejia-Alvarez, R. & Christensen, K. T. 2013 Wall-parallel stereo particle-image velocimetry measurements in the roughness sublayer of turbulent flow overlying highly irregular roughness. Phys. Fluids 25, 115109.Google Scholar
Mejia-Alvarez, R., Wu, Y. & Christensen, K. T. 2014 Observations of meandering superstructures in the roughness sublayer of a turbulent boundary layer. Intl J. Heat Fluid Flow 48, 43–51.Google Scholar
Monty, J. P., Hutchins, N., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.Google Scholar
Nadeem, M., Lee, J. H., Lee, J. & Sung, H. J. 2015 Turbulent boundary layers over sparsely-spaced rod-roughened walls. Intl J. Heat Fluid Flow 56, 16–27.Google Scholar
Oke, T. R. 1988 Street design and urban canopy layer climate. Energy Build. 11, 103–113.Google Scholar
Perret, L., Basley, J., Mathis, R. & Piquet, T. 2018 Boundary-Layer Meteorol. (submitted).Google Scholar
Perret, L., Piquet, T., Basley, J. & Mathis, R. 2017 Effects of plan area densities of cubical roughness elements on turbulent boundary layers. In ScienceConf, CFM.Google Scholar
Placidi, M. & Ganapathisubramani, B. 2017 Turbulent flow over large roughness elements: effect of frontal and plan solidity on turbulence statistics and structure. Boundary-Layer Meteorol. 167, 99–121.Google Scholar
Rao, K. N., Narasimha, R. & Narayanan, M. A. B. 1971 The ‘bursting’ phenomenon in a turbulent boundary layer. J. Fluid Mech. 48, 339.Google Scholar
Rivet, C.2014 Etude en soufflerie atmosphérique des interactions entre canopé urbaine et basse atmosphère par PIV stéréoscopique. PhD thesis, Ecole Centrale de Nantes.Google Scholar
Squire, D. T., Baars, W. J., Hutchins, N. & Marusic, I. 2016a Inner–outer interactions in rough-wall turbulence. J. Turbul. 17 (12), 1159–1178.Google Scholar
Squire, D. T., Morill-Winter, C., Hutchins, N., Schultz, M. P., Klewicki, J. C. & Marusic, I. 2016b Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers. J. Fluid Mech. 795, 210–240.Google Scholar
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.Google Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164, 476–490.Google Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.Google Scholar
Wu, O. & Christensen, K. T. 2010 Spatial structure of a turbulent boundary layer with irregular surface roughness. J. Fluid Mech. 655, 380–418.Google Scholar
Yao, Y. C., Huang, W. X. & Xu, C. X. 2018 Amplitude modulation and extreme events in turbulent channel flow. Acta Mechanica Sin. 34 (1), 1–9.Google Scholar
Zhong, Q., Li, D., Chen, Q. & Wang, X. 2015 Coherent structures and their interactions in smooth open channel flows. Environ. Fluid Mech. 15 (3), 653–672.Google Scholar