Skip to main content Accesibility Help
×
×
Home

Pressure gradient effects on the large-scale structure of turbulent boundary layers

  • Zambri Harun (a1) (a2), Jason P. Monty (a1), Romain Mathis (a1) (a3) and Ivan Marusic (a1)
Abstract

Research into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

Copyright
Corresponding author
Email address for correspondence: montyjp@unimelb.edu.au
References
Hide All
Abe, H., Kawamura, H. & Choi, H. 2004 Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to . Trans. ASME: J. Fluid Engng 126, 835843.
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of a turbulent boundary layer. J. Fluid Mech. 422, 153.
del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41L44.
del Álamo, J. C. & Jiménez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205213.
del Álamo, J. C. & Jiménez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 526.
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.
Aubertine, C. D. & Eaton, J. K. 2005 Turbulence development in a non-equilibrium turbulent boundary layer with mild adverse pressure gradient. J. Fluid Mech. 532, 345364.
Bailey, S. C. C., Hultmark, M., Smits, A. & Schultz, M. P. 2008 Azimuthal structure of turbulence in high Reynolds number pipe flow. J. Fluid Mech. 615, 121138.
Balakumar, B. J. & Adrian, R. J. 2007 Large and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. A 365, 665681.
Bandyopadhyay, P. R. & Hussain, A. K. M. F. 1984 The coupling between scales in shear flows. Phys. Fluids 27 (9), 22212228.
Bourassa, C. & Thomas, F. O. 2009 An experimental investigation of a highly accelerated turbulent boundary layer. J. Fluid Mech. 634, 359404.
Bradshaw, P. 1967a Inactive motion and pressure fluctuations in turbulent boundary layers. J. Fluid Mech. 30, 241258.
Bradshaw, P. 1967b The turbulence structure of equilibrium boundary layers. J. Fluid Mech. 29, 625645.
Chauhan, K., Ng, H. C. H. & Marusic, I. 2010 Empirical mode decomposition and Hilbert transforms for analysis of oil-film interferograms. Meas. Sci. Technol. 21, 105405, 113.
Chung, D. & McKeon, B. J. 2010 Large-eddy simulation of large-scale structures in long channel flow. J. Fluid Mech. 661, 341364.
DeGraaff, D. E. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319346.
Dengel, P. & Fernholz, H. H. 1990 An experimental investigation of an incompressible turbulent boundary layer in the vicinity of separation. J. Fluid Mech. 212, 615636.
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.
Dixit, S. A. & Ramesh, O. N. 2010 Large-scale structures in turbulent and reverse-transitional sink flow boundary layers. J. Fluid Mech. 649, 233273.
Fernholz, H. H. & Warnack, D. 1998 The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 1. The turbulent boundary layer. J. Fluid Mech. 359, 329356.
Ganapathisubramani, B., Hambleton, N., Hutchins, W. T., Longmire, E. K. & Marusic, I. 2005 Investigation of large-scale coherence in a turbulent boundary layer using two-point correlation. J. Fluid Mech. 524, 5780.
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 3546.
Grinvald, D. & Nikora, V. 1988 Rechnaya turbulentnost (River Turbulence). Hydrometeoizdat, Russia (in Russian).
Hambleton, W. T., Hutchins, N. & Marusic, I. 2006 Simultaneous orthogonal-plane particular image velocimetry measurements in a turbulent boundary layer. J. Fluid Mech. 560, 5364.
Hutchins, N. & Marusic, I. 2007a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.
Hutchins, N. & Marusic, I. 2007b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. A 365, 647664.
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.
Jones, M. B., Marusic, I. & Perry, A. E. 2001 Evolution and structure of sink flow turbulent boundary layers. J. Fluid Mech. 428, 127.
Jones, W. P. & Launder, B. E. 1972 Some properties of sink-flow turbulent boundary layers. J. Fluid Mech. 56, 337351.
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417422.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741773.
Krogstad, P.-A˚ & Skåre, P. E. 1995 Influence of a strong adverse pressure gradient on the turbulent structure in a boundary layer. Phys. Fluids 7, 20142024.
Kunkel, G. & 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.
Lee, J. H. & Sung, H. J. 2009 Structures in turbulent boundary layers subjected to adverse pressure gradients. J. Fluid Mech. 639, 101131.
Maciel, Y., Rossignol, K.-S. & Lemay, J. 2006 Self similarity in the outer region of adverse-pressure-gradient turbulent boundary layers. AIAA J. 44 (11), 24502464.
Marusic, I. & Heuer, W. D. C. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99, 4145.
Marusic, I. & Hutchins, N. 2007 Study of the log-layer structure in wall turbulence over a very large range of Reynolds number. Flow Turbul. Combust. 81, 115130.
Marusic, I., Mathis, R. & Hutchins, N. 2010 High Reynolds number effects in wall turbulence. Int. J. Heat Fluid Flow 31, 418428.
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.
Mathis, R., Hutchins, N. & Marusic, I. 2009a Large-scale amplitude modulation of the small-scale structures in turbulent boudary layers. J. Fluid Mech. 628, 311337.
Mathis, R., Monty, J. P, Hutchins, N. & Marusic, I. 2009b Comparison of large-scale amplitude modulation in turbulent boundary layers, pipes, and channel flows. Phys. Fluids 21 (11), 111703.
Metzger, M. M. & Klewicki, J. C. 2001 A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys. Fluids 13 (3), 692701.
Monty, J. P., Harun, Z. & Marusic, I. 2011 A parametric study of adverse pressure gradient turbulent boundary layers. Int. J. Heat Fluid Flow 32, 575585.
Monty, J. P., Hutchins, N., Ng, H. C. H. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431442.
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, 147156.
Na, Y. & Moin, P. 1998 Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 374, 379405.
Nagano, Y., Tagawa, M. & Tsuji, T. 1992 Effects of adverse pressure gradients on mean flows and turbulence statistics in a boundary layer. In Proceedings of Turbulent Shear Flows 8, pp. 721Berlin.
Nagano, Y., Tsuji, T. & Houra, T. 1998 Structure of turbulent boundary layer subjected to adverse pressure gradient. Int. J. Heat Fluid Flow 19, 563572.
Nagib, H. M. & Chauhan, K. A. 2008 Variations of von Kármán coefficient in canonical flows. Phys. Fluids 20, 101518.
Nickels, T. B., Marusic, I., Hafez, S. & Chong, M. S. 2005 Evidence of the law in a high-Reynolds-number turbulent boundary layer. Phys. Rev. Lett. 95, 074501.
Nikora, V., Nokes, R., Veale, W., Davidson, M. & Jirka, G. H. 2007 Large-scale turbulent structure of uniform shallow free-surface flows. Environ. Fluid Mech. 7 (2), 159172.
Perry, A. E., Marusic, I. & Jones, M. B. 2002 On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients. J. Fluid Mech. 461, 6191.
Perry, A. E., Marusic, I. & Li, J. D. 1994 Wall turbulence closure based on classical similarity laws and the attached eddy hypothesis. Phys. Fluids 6 (2), 1024.
Pope, S. B. 2000 Turbulent flows. Cambridge University Press.
Rahgozar, S. & Maciel, Y. 2011 Low- and high-speed structures in the outer region of an adverse-pressure-gradient turbulent boundary layer. Experimental Thermal and Fluid Science 35 (8), 15751587.
Rao, K. N., Narasimha, R. & Badri Narayanan, M. A. 1971 The ‘bursting’ phenomena in a turbulent boundary layer. J. Fluid Mech. 48, 339352.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601639.
Skote, M. & Henningson, D. S. 2002 Direct numerical simulation of a seperated turbulent boundary layer. J. Fluid Mech. 471, 107136.
Skote, M., Henningson, D. S. & Henkes, R. A. W. M. 1998 Direct numerical simulation of self-similar turbulent boundary layers in adverse pressure gradients. Flow Turbulence Combustion 60, 4785.
Skåre, P. E. & Krogstad, P.-A˚. 1994 A turbulent equilibrium boundary layer near separation. J. Fluid Mech. 272, 319348.
Spalart, P. R. & Coleman, G. N. 1997 Numerical study of a separation bubble with heat transfer. Eur. J. Mech. B Fluids 16, 169189.
Spalart, P. R. & Watmuff, J. H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradient. J. Fluid Mech. 249, 337371.
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 3774.
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97120.
Townsend, A. A. 1976 The structure of turbulent shear flow, 2nd edn. Cambridge University Press.
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

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed