Experiments in Fluids

, 54:1481 | Cite as

Phase relationships between large and small scales in the turbulent boundary layer

Research Article

Abstract

The apparent amplitude modulation effect between large- and small-scale motions in the turbulent boundary layer, including both streamwise and wall-normal velocity components, is explored by cross-correlation techniques. Single-point hotwire and planar PIV measurements are employed to consider the envelopes of small-scale fluctuations in both directions and their correlation with the fluctuations of large-scale motions in the streamwise direction. The degree of correlation is interpreted as a measure of phase lag between the different scale motions, and these phase measurements are used to demonstrate that the fluctuations in the envelope of small-scale motions in both directions tend to lead corresponding fluctuations in the large scales in the streamwise direction. The cospectral density of the cross-correlation between the different scales is used to identify the particular large-scale motions dominant in the modulation effect, and it is shown that the dominant interacting (or ‘modulating’) scale corresponds in size to the very large-scale motions observed in internal flows but not normally observed in the outer region of the boundary layer.

References

  1. Bandyopadhyay PR, Hussain AKMF (1984) The coupling between scales in shear flows. Phys Fluids 27(9):2221–2228CrossRefGoogle Scholar
  2. Bernardini M, Pirozzoli S (2011) Inner/outer layer interactions in turbulent boundary layers: a refined measure for the large-scale amplitude modulation mechanism. Phys Fluids 23(6):061701Google Scholar
  3. Chung D, McKeon BJ (2010) Large-eddy simulation of large-scale structures in long channel flow. J Fluid Mech 661:341–364MATHCrossRefGoogle Scholar
  4. Dennis DJC, Nickels TB (2008) On the limitations of Taylor’s hypothesis in constructing long structures in a turbulent boundary layer. J Fluid Mech 614:197–206MathSciNetMATHCrossRefGoogle Scholar
  5. Falco RE (1977) Coherent motions in the outer region of turbulent boundary layers. Phys Fluids 20:124–132CrossRefGoogle Scholar
  6. Guala M, Metzger M, McKeon BJ (2011) Interactions across the turbulent boundary layer at high Reynolds number. J Fluid Mech 666:573–604MATHCrossRefGoogle Scholar
  7. Hutchins N, Marusic I (2007) Large-scale influences in near-wall turbulence. Philos Trans R Soc 365:647–664MATHCrossRefGoogle Scholar
  8. Hutchins N, Monty JP, Ganapathisubramani B, Ng HCH, Marusic I (2011) Three-dimensional conditional structure of a high-Reynolds-number turbulent boundary layer. J Fluid Mech 673:255–285MATHCrossRefGoogle Scholar
  9. Jacobi I, McKeon BJ (2011a) New perspectives on the impulsive roughness-perturbation of a turbulent boundary layer. J Fluid Mech 677:179–203MATHCrossRefGoogle Scholar
  10. Jacobi I, McKeon BJ (2011b) Dynamic roughness-perturbation of a turbulent boundary layer. J Fluid Mech 688:258–296MATHCrossRefGoogle Scholar
  11. Kim KC, Adrian RJ (1999) Very large-scale motion in the outer layer. Phys Fluids 11(2):417–422MathSciNetMATHCrossRefGoogle Scholar
  12. Kovasznay LSG, Kibens V, Blackwelder RF (1970) Large-scale motion in the intermittent region of a turbulent boundary layer. J Fluid Mech 41(2):283–325CrossRefGoogle Scholar
  13. Krogstad PÅ, Kaspersen JH, Rimestad S (1998) Convection velocities in a turbulent boundary layer. Phys Fluids 10(4):949–957Google Scholar
  14. Lehew J, Guala M, McKeon BJ (2011) A study of the three-dimensional spectral energy distribution in a zero pressure gradient turbulent boundary layer. Exp Fluids 51:997–1012Google Scholar
  15. Lyons RG (2011) Understanding digital signal processing, 3rd edn. Prentice Hall, Upper Saddle River, NJGoogle Scholar
  16. Marusic I, Mathis R, Hutchins N (2010) Predictive model for wall-bounded turbulent flow. Science 329(5988):193–196MathSciNetMATHCrossRefGoogle Scholar
  17. Mathis R, Hutchins N, Marusic I (2009a) Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J Fluid Mech 628:311–337MATHCrossRefGoogle Scholar
  18. Mathis R, Monty JP, Hutchins N, Marusic I (2009b) Comparison of large-scale amplitude modulation in turbulent boundary layers, pipes, and channel flows. Phys Fluids 21:111703Google Scholar
  19. Mathis R, Marusic I, Hutchins N, Sreenivasan KR (2011) The relationship between the velocity skewness and the amplitude modulation of the small scale by the large scale in turbulent boundary layers. Phys Fluids 23:121702Google Scholar
  20. Monty JP, Hutchins N, Ng HCH, Marusic I, Chong MS (2009) A comparison of turbulent pipe, channel and boundary layer flows. J Fluid Mech 632:431–442MATHCrossRefGoogle Scholar
  21. Perry AE, Henbest S, Chong MS (1986) A theoretical and experimental study of wall turbulence. J Fluid Mech 165:163–199Google Scholar
  22. Rodgers JL, Nicewander WA (1988) Thirteen ways to look at the correlation coefficient. Am Stat 42(1):59–66CrossRefGoogle Scholar
  23. Schlatter P, Örlü R (2010) Quantifying the interaction between large and small scales in wall-bounded turbulent flows: a note of caution. Phys Fluids 22:051704Google Scholar
  24. Strader II NR (1980) Effects of subharmonic frequencies on DFT coefficients. Proceedings of the IEEE 68(2):285–286Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Graduate Aerospace LaboratoriesCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of Mechanical and Aerospace EngineeringPrinceton UniversityPrincetonUSA

Personalised recommendations