Scaling of Adverse-Pressure-Gradient Turbulent Boundary Layers in Near-Equilibrium Conditions

  • Ricardo VinuesaEmail author
  • Alexandra Bobke
  • Ramis Örlü
  • Philipp Schlatter
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 196)


Well-resolved large-eddy simulations are used to study adverse-pressure-gradient (APG) turbulent boundary layers (TBLs) under near-equilibrium conditions. In particular, we focus on two near-equilibrium cases where the power-law freestream velocity distribution is adjusted in order to produce long regions with a constant value of the Clauser pressure-gradient parameter \(\beta \). In the first case we obtain an APG TBL with a constant value of \(\beta \simeq 1\) over 37 average boundary-layer thicknesses, and in the second one a constant value of \(\beta \simeq 2\) for around 28 average boundary-layer thicknesses. The scaling law suggested by Kitsios et al. (Int J Heat Fluid Flow 61:117–128, 2016, [10]), proposing the edge velocity and the displacement thickness as scaling parameters, was tested on the two constant-pressure-gradient parameter cases. The mean velocity and Reynolds-stress profiles were found to be dependent on the downstream development, a conclusion in agreement with classical theory.


  1. 1.
    A.A. Townsend, The Structure of Turbulent Shear Flow (Cambridge Univ. Press, Cambridge, UK, 1956)zbMATHGoogle Scholar
  2. 2.
    G.L. Mellor, D.M. Gibson, Equilibrium turbulent boundary layers. J. Fluid Mech. 24, 225–253 (1966)CrossRefGoogle Scholar
  3. 3.
    P. Schlatter, R. Örlü, Q. Li, G. Brethouwer, J.H.M. Fransson, A.V. Johansson, P.H. Alfredsson, D.S. Henningson, Turbulent boundary layers up to \({Re}_\theta =2500\) studied through simulation and experiment. Phys. Fluids 21, 051702 (2009)CrossRefzbMATHGoogle Scholar
  4. 4.
    S.C.C. Bailey, M. Hultmark, J.P. Monty, P.H. Alfredsson, M.S. Chong, R.D. Duncan, J.H.M. Fransson, N. Hutchins, I. Marusic, B.J. Mckeon, H.M. Nagib, R. Örlü, A. Segalini, A.J. Smits, R. Vinuesa, Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes. J. Fluid Mech. 715, 642–670 (2013)CrossRefzbMATHGoogle Scholar
  5. 5.
    P.E. Skåre, P.-Å. Krogstad, A turbulent equilibrium boundary layer near separation. J. Fluid Mech. 272, 319–348 (1994)CrossRefGoogle Scholar
  6. 6.
    M. Skote, D.S. Henningson, Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 471, 107–136 (2002)CrossRefzbMATHGoogle Scholar
  7. 7.
    P. Schlatter, R. Örlü, Turbulent boundary layers at moderate Reynolds numbers. Inflow length and tripping effects. J. Fluid Mech. 710, 5–34 (2012)CrossRefzbMATHGoogle Scholar
  8. 8.
    R. Vinuesa, P.H. Rozier, P. Schlatter, H.M. Nagib, Experiments and computations of localized pressure gradients with different history effects. AIAA J. 55, 368–384 (2014)CrossRefGoogle Scholar
  9. 9.
    V. Kitsios, C. Atkinson, J.A. Sillero, G. Borrell, A.G. Gungor, J. Jiménez, J. Soria, Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer. Int. J. Heat Fluid Flow 61, 129–136 (2016)CrossRefGoogle Scholar
  10. 10.
    S.M. Hosseini, R. Vinuesa, P. Schlatter, A. Hanifi, D.S. Henningson, Direct numerical simulation of the flow around a wing section at moderate Reynolds number. Int. J. Heat Fluid Flow 61, 117–128 (2016)CrossRefGoogle Scholar
  11. 11.
    A. Bobke, R. Vinuesa, R. Örlü, P. Schlatter, Large-eddy simulations of adverse pressure gradient turbulent boundary layers. J. Phys. Conf. Ser. 708, 012012 (2016)CrossRefGoogle Scholar
  12. 12.
    M. Chevalier, P. Schlatter, A. Lundbladh, D.S. Henningson, SIMSON a pseudospectral solver for incompressible boundary layer. TRITA-MEK 2007:07, Technical Report, KTH Mechanics (2007)Google Scholar
  13. 13.
    P. Schlatter, S. Stolz, L. Kleiser, LES of transitional flows using the approximate deconvolution model. Int. J. Heat Fluid Flow 25, 549–558 (2004)CrossRefGoogle Scholar
  14. 14.
    G. Eitel-Amor, R. Örlü, P. Schlatter, Simulation and validation of a spatially evolving turbulent boundary layer up to \(Re_{\theta }= 8300\). Int. J. Heat Fluid Flow 47, 57–69 (2014)CrossRefGoogle Scholar
  15. 15.
    R. Vinuesa, A. Bobke, R. Örlü, P. Schlatter, On determining characteristic length scales in pressure-gradient turbulent boundary layers. Phys. Fluids 28, 055101 (2016)CrossRefGoogle Scholar
  16. 16.
    C. Atkinson, A.J. Buchner, M. Eisfelder, V. Kitsios, J. Soria, Time-resolved PIV measurements of a self-similar adverse pressure gradient turbulent boundary layer. in, Proc. 18th Intl Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics, Lisbon, Portugal (2016)Google Scholar
  17. 17.
    A. Bobke, R. Vinuesa, R. Örlü, P. Schlatter, History effects and near equilibrium in adverse-pressure gradient turbulent boundary layers. J. Fluid Mech. 820, 667–692 (2017)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Ricardo Vinuesa
    • 1
    • 2
    Email author
  • Alexandra Bobke
    • 1
    • 2
  • Ramis Örlü
    • 1
  • Philipp Schlatter
    • 1
    • 2
  1. 1.Linné FLOW Centre, KTH MechanicsStockholmSweden
  2. 2.Swedish e-Science Research Centre (SeRC)StockholmSweden

Personalised recommendations