Hostname: page-component-7479d7b7d-q6k6v Total loading time: 0 Render date: 2024-07-13T15:42:01.707Z Has data issue: false hasContentIssue false
  • English
  • Français

On the dynamical relevance of coherent vortical structures in turbulent boundary layers

Published online by Cambridge University Press:  07 April 2010

SERGIO PIROZZOLI ,
MATTEO BERNARDINI  and
FRANCESCO GRASSO
SERGIO PIROZZOLI*
Affiliation:
Dipartimento di Meccanica e Aeronautica, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Roma, Italy
MATTEO BERNARDINI
Affiliation:
Dipartimento di Meccanica e Aeronautica, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Roma, Italy
FRANCESCO GRASSO
Affiliation:
Dipartimento di Meccanica e Aeronautica, Università di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Roma, Italy
*
†Email address for correspondence: sergio.pirozzoli@uniroma1.it
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamical relevance of vortex tubes and vortex sheets in a wall-bounded supersonic turbulent flow at Mach number M = 2 and Reynolds number Reθ ≈ 1350 is quantitatively analysed. The flow in the viscous sublayer and in the buffer region is characterized by intense, elongated vorticity tongues forming a shallow angle with respect to the wall, whose characteristic length is O(200) wall units and whose size in the cross-stream direction is O(50) wall units. The formation of vortex tubes takes place starting from y+ ≈ 10, and it is mainly associated with the roll-up and the interaction of vortex sheets. The analysis of the non-local dynamical effect of tubes and sheets suggests that the latter have a more important collective effect, being closely associated with low-speed streaks, and being responsible for a substantial contribution to the mean momentum balance and to the production of turbulence kinetic energy and enstrophy.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 325 - 349
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Acarlar, M. S. & Smith, C. R. 1986 A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J. Fluid Mech. 175, 1–41.CrossRefGoogle Scholar
Acarlar, M. S. & Smith, C. R. 1987 A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection. J. Fluid Mech. 175, 43–83.CrossRefGoogle Scholar
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.CrossRefGoogle Scholar
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, 1–54.CrossRefGoogle Scholar
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, 329–358.CrossRefGoogle Scholar
Aris, R. 1990 Vectors, Tensors and the Basic Equations of Fluid Mechanics. Dover.Google Scholar
Baker, G. R. & Shelley, M. J. 1990 On the connection between thin vortex layers and vortex sheets. J. Fluid Mech. 215, 161–194.CrossRefGoogle Scholar
Bermejo-Moreno, I., Pullin, D. I. & Horiuti, K. 2009 Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence. J. Fluid Mech. 620, 121–166.CrossRefGoogle Scholar
Brandt, L. & de Lange, H. C. 2008 Streak interactions and breakdown in boundary layer flows. Phys. Fluids 20, 024107.CrossRefGoogle Scholar
Cadot, O., Douady, S. & Couder, Y. 1995 Characterization of the low-pressure filaments in a three-dimensional turbulent shear layer. Phys. Fluids 7, 630–646.CrossRefGoogle Scholar
Carlier, J. & Stanislas, M. 2005 Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry. J. Fluid Mech. 535, 143–188.CrossRefGoogle Scholar
Chong, M. S., Soria, J., Perry, E., Chacin, J., Cantwell, B. J. & Na, Y. 1998 Turbulence structures of wall-bounded shear flows found using DNS data. J. Fluid Mech. 357, 225–247.CrossRefGoogle Scholar
Das, S. K., Tanahashi, M. & Shoji, K. 2006 Statistical properties of coherent fine eddies in wall-bounded turbulent flows by direct numerical simulation. Teor. Comput. Fluid Dyn. 20, 55–71.CrossRefGoogle Scholar
Douady, S., Couder, Y. & Brachet, M. E. 1991 Direct observation of the intermittency of intense vorticity filaments in turbulence. Phys. Rev. Lett. 67, 983–986.CrossRefGoogle ScholarPubMed
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 35–46.CrossRefGoogle Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2006 Experimental investigation of vortex properties in a turbulent boundary layer. Phys. Fluids 18, 055105.CrossRefGoogle Scholar
Head, M. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297–338.CrossRefGoogle Scholar
Hirasaki, G. J. & Hellums, J. D. 1970 Boundary conditions on the vector and scalar potentials in viscous three-dimensional hydrodynamics. Qu. App. Math. 28, 293–296.CrossRefGoogle Scholar
Horiuti, K. & Fujisawa, T. 2008 The multi-mode stretched spiral vortex in homogeneous isotropic turbulence. J. Fluid Mech. 595, 341–366.CrossRefGoogle Scholar
Horiuti, K. & Takagi, Y. 2005 Identification method for vortex sheet structures in turbulent flows. Phys. Fluids 17, 121703.CrossRefGoogle Scholar
Jiménez, J., Moin, P., Moser, R. & Keefe, L. 1988 Ejection mechanisms in the sublayer of a turbulent channel. Phys. Fluids 31, 1311–1313.CrossRefGoogle Scholar
Jiménez, J. & Wray, A. A. 1998 On the characteristics of vortex filaments in isotropic turbulence. J. Fluid Mech. 373, 255–285.CrossRefGoogle Scholar
Jiménez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.CrossRefGoogle Scholar
Johansson, A. V., Alfredsson, P. H. & Eckelmann, H. 1987 On the evolution of shear-layer structures in near-wall turbulence. In Advances in Turbulence, Proc. First European Turbulence Conference (ed. Comte-Bellot, G. & Mathieu, J.), pp. 383–390. Springer.Google Scholar
Johansson, A. V., Alfredsson, P. H. & Kim, J. 1991 Evolution and dynamics of shear-layer structures in near-wall turbulence. J. Fluid Mech. 224, 579–599.CrossRefGoogle Scholar
Kendall, M. G., Stuart, A., Ord, K. J. & Arnold, S. 1999 Kendall's Advanced Theory of Statistics: Volume 2A: Classical Inference and the Linear Model (Kendall's Library of Statistics), 6th ed. Arnold.Google Scholar
Klewicki, J. C. 1997 Self-sustaining traits of near-wall motions underlying boundary layer stress transport. In Self-sustaining Mechanisms of Wall Turbulence (ed. Panton, R. L.), vol. 15, pp. 135–166. Computational Mechanics Publications.Google Scholar
Klewicki, J. C. & Hirschi, C. R. 2004 Flow field properties local to near-wall shear layers in a low Reynolds number turbulent boundary layer. Phys. Fluids 16, 4163–4176.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, W. C. & Runstadler, F. A. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
Labraga, L., Lagraa, B., Mazouz, A. & Keirsbulck, L. 2002 Propagation of shear-layer structures in the near-wall region of a turbulent boundary layer. Exp. Fluids 33, 670–676.CrossRefGoogle Scholar
Liu, Z.-C., Landreth, C. C., Adrian, R. J. & Hanratty, T. J. 1991 High resolution measurement of turbulent structure in a channel with particle image velocimetry. Exp. Fluids 10, 301–312.CrossRefGoogle Scholar
Marusic, I. 2001 On the role of large-scale structures in wall turbulence. Phys. Fluids 13, 735–743.CrossRefGoogle Scholar
Passot, T., Politano, H., Sulem, P. L., Angilella, J. R. & Meneguzzi, M. 1995 Instability of strained vortex layers and vortex tube formation in homogeneous turbulence. J. Fluid Mech. 282, 313–338.CrossRefGoogle Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Grasso, F. 2008 Characterization of coherent vortical structures in a supersonic turbulent boundary layer. J. Fluid Mech. 613, 205–231.CrossRefGoogle Scholar
Pirozzoli, S., Grasso, F. & Gatski, T. B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2.25. Phys. Fluids 16 (3), 530–545.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Ruetsch, G. R. & Maxey, M. R. 1992 The evolution of small-scale structures in homogeneous isotropic turbulence. Phys. Fluids A 4, 2747–2760.CrossRefGoogle Scholar
Sandham, N. D., Yao, Y. F. & Lawal, A. A. 2003 Large-eddy simulation of transonic flow over a bump. Intl J. Heat Fluid Flow 24, 584–595.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.CrossRefGoogle Scholar
She, Z.-S., Jackson, E. & Orszag, S. A. 1990 Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344, 226.CrossRefGoogle Scholar
Stanislas, M., Perret, L. & Foucaut, J.-M. 2008 Vortical structures in the turbulent boundary layer: a possible route to a universal representation. J. Fluid Mech. 602, 327–382.CrossRefGoogle Scholar
Tanahashi, M., Kang, S.-J., Shiokawa, S. & Miyauchi, T. 2004 Scaling laws of fine scale eddies in turbulent channel flows up to Re τ = 800. Intl J. Heat Fluid Flow 25, 331–340.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT.CrossRefGoogle Scholar
Theodorsen, T. 1952 Mechanism of turbulence. In Proceedings of the Second Midwestern Conf. on Fluid Mechanics, pp. 17–19. Ohio State University, Columbus, Ohio.Google Scholar
Tsinober, A. 1998 Is concentrated vorticity that important? Eur. J. Mech. B. Fluids 4, 421–449.CrossRefGoogle Scholar
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1–20.CrossRefGoogle Scholar
Wark, C. E. & Nagib, H. M. 1991 Experimental investigation of coherent structures in turbulent boundary layers. J. Fluid Mech. 230, 183–208.CrossRefGoogle Scholar
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 5–41.CrossRefGoogle Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar