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Turbulent boundary layers over permeable walls: scaling and near-wall structure

Published online by Cambridge University Press:  10 October 2011

C. Manes ,
D. Poggi  and
L. Ridolfi
C. Manes*
Affiliation:
Politecnico di Torino, Dipartimento di Idraulica, Trasporti ed Infrastrutture Civili (DITIC), Corso Duca degli Abruzzi, 10129 Torino, Italy
D. Poggi
Affiliation:
Politecnico di Torino, Dipartimento di Idraulica, Trasporti ed Infrastrutture Civili (DITIC), Corso Duca degli Abruzzi, 10129 Torino, Italy
L. Ridolfi
Affiliation:
Politecnico di Torino, Dipartimento di Idraulica, Trasporti ed Infrastrutture Civili (DITIC), Corso Duca degli Abruzzi, 10129 Torino, Italy
*
†Email address for correspondence: [email protected]
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Abstract

This paper presents an experimental study devoted to investigating the effects of permeability on wall turbulence. Velocity measurements were performed by means of laser Doppler anemometry in open channel flows over walls characterized by a wide range of permeability. Previous studies proposed that the von Kármán coefficient associated with mean velocity profiles over permeable walls is significantly lower than the standard values reported for flows over smooth and rough walls. Furthermore, it was observed that turbulent flows over permeable walls do not fully respect the widely accepted paradigm of outer-layer similarity. Our data suggest that both anomalies can be explained as an effect of poor inner–outer scale separation if the depth of shear penetration within the permeable wall is considered as the representative length scale of the inner layer. We observed that with increasing permeability, the near-wall structure progressively evolves towards a more organized state until it reaches the condition of a perturbed mixing layer where the shear instability of the inflectional mean velocity profile dictates the scale of the dominant eddies. In our experiments such shear instability eddies were detected only over the wall with the highest permeability. In contrast attached eddies were present over all the other wall conditions. On the basis of these findings, we argue that the near-wall structure of turbulent flows over permeable walls is regulated by a competing mechanism between attached and shear instability eddies. We also argue that the ratio between the shear penetration depth and the boundary layer thickness quantifies the ratio between such eddy scales and, therefore, can be used as a diagnostic parameter to assess which eddy structure dominates the near-wall region for different wall permeability and flow conditions.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Turbulent Flows: Shear layer turbulence Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 687 , 25 November 2011 , pp. 141 - 170
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

‡

Present address: Politecnico di Torino, Dipartimento di Idraulica, Trasporti ed Infrastrutture Civili (DITIC), Corso Duca degli Abruzzi, Torino, Italy.

References

1. Allen, J. J., Shockling, M. A., Kunkel, G. J. & Smits, A. J. 2007 Turbulent flow in smooth and rough pipes. Phil. Trans. R. Soc. Lond. 365, 699–714.Google ScholarPubMed
2. Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562, 35–72.Google Scholar
3. Clifton, A., Manes, C., Rüedi, J. D., Guala, M. & Lehning, M. 2008 On shear-driven ventilation of snow. Boundary-Layer Meteorol. 126, 249–261.CrossRefGoogle Scholar
4. De Alamo, J. C. & Jimenez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 5–26.Google Scholar
5. DeGraaff, D. B. & Eaton, J. K. 2001 A high-resolution Laser Doppler Anemometer: design, qualification and uncertainty. Exp. Fluids 30, 522–530.CrossRefGoogle Scholar
6. Detert, M., Nikora, V. & Jirka, G. H. 2010 Synoptic velocity and pressure fields at the water-sediment interface of streambeds. J. Fluid Mech. 660, 55–86.CrossRefGoogle Scholar
7. Finnigan, J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519–571.Google Scholar
8. Finnigan, J. J., Shaw, R. H. & Patton, E. G. 2009 Turbulent structure above a vegetation canopy. J. Fluid Mech. 637, 387–424.Google Scholar
9. George, W. K. 2007 Is there a universal log law for turbulent wall-bounded flows?. Phil. Trans. R. Soc. Lond 365, 789–806.Google Scholar
10. George, W. K. & Castillo, L. 1997 Zero-pressure-gradient turbulent boundary layer. Appl. Mech. Rev. 50, 11.CrossRefGoogle Scholar
11. Ghisalberti, M. 2009 Obstructed shear flows: similarities across systems and scales. J. Fluid Mech. 641, 51–61.Google Scholar
12. Ghisalberti, M. & Nepf, H. M. 2002 Mixing layers and coherent structures in vegetated aquatic flows. J. Geophys. Res. 107 (C2), 3011.Google Scholar
13. Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.CrossRefGoogle Scholar
14. 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
15. Hahn, S., Je, J. & Choi, H. 2002 Turbulent channel flow with permeable walls. J. Fluid Mech. 450, 259–285.Google Scholar
16. Hildebrand, T. & Ruegsegger, P. 1997 EA new method for the model-independent assesment of thickness in three-dimensional images. J. Microsc.-Oxford 185 (Part 1), 67–75.CrossRefGoogle Scholar
17. Hunt, J. C. R. & Morrison, J. F. 2000 Eddy structure in turbulent boundary layers. Eur. J. Mech. B/Fluids 19 (5), 673–694.CrossRefGoogle Scholar
18. Hutchins, N. & Marusic, I. 2007 Large-scale influences in near wall turbulence. Phil. Trans. R. Soc. 365, 647–664.Google Scholar
19. Jackson, P. S. 1981 On the displacement height in the logarithmic velocity profile. J. Fluid Mech. 111, 15–25.Google Scholar
20. Jimenez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
21. Katul, G., Poggi, D., Cava, D. & Finnigan, J. 2006 The relative importance of ejections and sweeps to momentum transfer in the atmospheric boundary layer. Boundary-Layer Meteorol. 120, 367–375.Google Scholar
22. Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11, 417–422.CrossRefGoogle Scholar
23. Kironoto, B. A. & Graf, W. H. 1994 Turbulence characteristics in rough uniform open-channel flow. Proc. Inst. Civil Engrs Waters Maritime Energy 106, 333–334.Google Scholar
24. Krogstad, P. A., Antonia, R. A. & Browne, L. W. B. 1992 Comparison between rough-and smooth-wall turbulent boundary layers. J. Fluid Mech. 245, 519–617.Google Scholar
25. 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, 375–402.CrossRefGoogle Scholar
26. Leonardi, S. & Castro, I. P. 2010 Channel flow over large cube roughness: a direct numerical simulation study. J. Fluid Mech. 651, 519–539.CrossRefGoogle Scholar
27. Manes, C., Pokrajac, D., McEwan, I. & Nikora, V. 2009 Turbulence structure of open channel flows over permeable and impermeable beds: a comparative study. Phys. Fluids 21, 125109.CrossRefGoogle Scholar
28. Manes, C., Pokrajac, D., Nikora, V., Ridolfi, L. & Poggi, D. 2011 Turbulent friction in flows over permeable walls. Geophys. Res. Lett. 38, L03402.Google Scholar
29. Marusic, I., Mckeon, B. J., Monkevitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22, 065103.CrossRefGoogle Scholar
30. 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, 431–442.Google Scholar
31. Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147–156.Google Scholar
32. Nickels, T. B., Marusic, I., Hafez, S., Hutchins, N. & Chong, M. S. 2007 Some predictions of the attached eddy model for a high Reynolds number boundary layer. Phil. Trans. R. Soc. Lond. 365, 807–822.Google Scholar
33. Nikora, V. 2010 Hydrodynamics of aquatic ecosystems an interface between ecology, biomechanics and environmental fluid mechanics. River Research and Applications 26, 367–384.CrossRefGoogle Scholar
34. Nikora, V. & Goring, D. 2000 Flow turbulence over fixed and weakly mobile gravel beds. J. Hydraul. Engng 126, 9.Google Scholar
35. Poggi, D., Porporato, A. & Ridolfi, L. 2002 An experimental contribution to near-wall measurements by means of a special laser Doppler anemometry technique. Exp. Fluids 32 (3), 366–375.Google Scholar
36. Poggi, D., Porporato, A., Ridolfi, L., Albertson, J. D. & Katul, G. G. 2004 The effect of vegetation density on canopy sub-layer turbulence. Boundary-Layer Meteorol. 111, 565–587.CrossRefGoogle Scholar
37. Raupach, M. R. 1981 Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers. J. Fluid Mech. 108, 363–382.Google Scholar
38. Raupach, M. R., Finnigan, J. J. & Brunet, Y 1996 Coherent eddies and turbulence in vegetation canopies: the mixing layer analogy. Boundary-Layer Meteorol. 78, 351–382.Google Scholar
39. Sarkar, S. & Dey, S. 2010 Double-averaging turbulence characteristics in flows over a gravel bed. J. Hydraul. Res. 48 (6), 801–809.CrossRefGoogle Scholar
40. Schneebeli, M. & Sokratov, S. 2004 Tomography of temperature gradient metamorphism of snow and associated changes in heat conductivity. Hydrol. Process. 18, 3655–3665.CrossRefGoogle Scholar
41. Suga, K., Matsumura, Y., Ashitaka, Y., Tominaga, S. & Kaneda, M. 2010 Effects of wall permeability on turbulence. Intl J. Heat Fluid Flow 31 (6), 974–984.Google Scholar
42. Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
43. Wesson, K. H., Katul, G. G. & Siqueira, M. 2003 Quantifying organization of atmospheric turbulent motion using nonlinear time series analysis. Boundary-Layer Meteorol. 106 (3), 507–525.Google Scholar
44. White, B. L. & Nepf, H. M. 2007 Shear instability and coherent structures in shallow flow adjacent to a porous layer. J. Fluid Mech. 593, 1–32.Google Scholar
45. Wosnik, M., Castillo, L. & George, W. K. 2000 A theory for turbulent pipe and channel flows. J. Fluid Mech. 421, 115–145.Google Scholar
46. Zagni, A. F. E. & Smith, K. V. H. 1976 Channel flow over permeable beds of graded spheres. J. Hydraul. Div, 102 (HY2).Google Scholar