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Spatial organisation of velocity structures for large passive scalar gradients

Published online by Cambridge University Press:  06 January 2020

Angeliki Laskari Open the ORCID record for Angeliki Laskari [Opens in a new window] ,
T. Saxton-Fox Open the ORCID record for T. Saxton-Fox [Opens in a new window]  and
B. J. McKeon
Angeliki Laskari*
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91106, USA
T. Saxton-Fox
Affiliation:
Department of Aerospace Engineering, University of Illinois, Urbana, IL 61801, USA
B. J. McKeon
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91106, USA
*
†Email address for correspondence: [email protected]
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Abstract

Velocity structures associated with large streamwise density gradients in an incompressible turbulent boundary layer (with air as the working fluid, $Pr=0.71$) are analysed experimentally using planar image velocimetry and aero-optic measurements. The resulting flow topologies for the velocity fluctuations associated with large negative and positive density gradients are in excellent agreement with results for coolings and heatings in time, respectively (Antonia & Fulachier, J. Fluid Mech., vol. 198, 1989, pp. 429–451). The current results are complimentary to those from Saxton-Fox et al. (AIAA J., vol. 57 (7), 2019, pp. 2828–2839), on the signature of the vertical velocity structures associated with large density gradients. In the present work, these structures are shown to exhibit a sign change, consistent with the scalar gradient, and are localised in the wall-normal direction with an average height of approximately $0.1\unicode[STIX]{x1D6FF}$, almost constant for increasing distance from the wall. The corresponding small-scale streamwise fluctuations also exhibit a consistent sign change, which is found to originate, on average, from upstream leaning structures. The emerging picture for the velocity field is then that of a multiscale phenomenon, where small-scale structures, responsible for large optical aberrations, are superimposed on the back of large-scale bulge-like structures that are known to populate the outer layers. The proposed conceptual model is consistent with early ideas of ‘typical’ eddies (Falco, Phys. Fluids, vol. 20 (10), 1977, pp. S124–S132), the hairpin vortex model and associated shear layers (Adrian et al., J. Fluid Mech., vol. 422, 2000, pp.1–54), as well as with notions of multiscale velocity organisation in shear layers (Klewicki & Hirschi, Phys. Fluids, vol. 16 (11), 2004, pp. 4163–4176; Saxton-Fox et al. 2019), and it provides new insight into the geometry of the small-scale velocity structures.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , A33
Copyright
© 2020 Cambridge University Press

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References

Abe, H., Antonia, R. A. & Kawamura, H. 2009 Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow. J. Fluid Mech. 627, 1–32.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
Antonia, R. A., Abe, H. & Kawamura, H. 2009 Analogy between velocity and scalar fields in a turbulent channel flow. J. Fluid Mech. 628, 241–268.CrossRefGoogle Scholar
Antonia, R. A., Chambers, A. J., Friehe, C. A. & Van Atta, C. W. 1979 Temperature ramps in the atmospheric surface layer. J. Atmos. Sci. 36 (1), 99–108.2.0.CO;2>CrossRefGoogle Scholar
Antonia, R. A. & Fulachier, L. 1989 Topology of a turbulent boundary layer with and without wall suction. J. Fluid Mech. 198, 429–451.CrossRefGoogle Scholar
Antonia, R. A., Fulachier, L., Krishnamoorthy, L. V., Benabid, T. & Anselmet, F. 1988a Influence of wall suction on the organized motion in a turbulent boundary layer. J. Fluid Mech. 190, 217–240.CrossRefGoogle Scholar
Antonia, R. A., Krishnamoorthy, L. V. & Fulachier, L. 1988b Correlation between the longitudinal velocity fluctuation and temperature fluctuation in the near-wall region of a turbulent boundary layer. Intl J. Heat Mass Transfer 31 (4), 723–730.CrossRefGoogle Scholar
Antonia, R. A., Rajagopalan, S., Subramanian, C. S. & Chambers, A. J. 1982 Reynolds-number dependence of the structure of a turbulent boundary layer. J. Fluid Mech. 121, 123–140.CrossRefGoogle Scholar
Antonia, R. A. & Van Atta, C. W. 1978 Structure functions of temperature fluctuations in turbulent shear flows. J. Fluid Mech. 84 (3), 561–580.CrossRefGoogle Scholar
Antonia, R. A. & Van Atta, C. W. 1979 Skewness of spatial derivatives of temperature in a turbulent boundary layer. Phys. Fluids 22 (12), 2430–2431.CrossRefGoogle Scholar
Baars, W. J., Hutchins, N. & Marusic, I. 2017 Reynolds number trend of hierarchies and scale interactions in turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 375 (2089), 20160077.Google ScholarPubMed
Balakumar, B. J. & Adrian, R. J. 2007 Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. Math. Phys. Engng Sci. 365 (1852), 665–681.CrossRefGoogle ScholarPubMed
Bisset, D. K., Antonia, R. A. & Raupach, M. R. 1991 Topology and transport properties of large scale organized motion in a slightly heated rough wall boundary layer. Phys. Fluids A 3 (9), 2220–2228.CrossRefGoogle Scholar
Chen, C.-H. P. & Blackwelder, R. F. 1978 Large-scale motion in a turbulent boundary layer: a study using temperature contamination. J. Fluid Mech. 89, 1–31.CrossRefGoogle Scholar
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aeronaut. Sci. 21 (2), 91–108.CrossRefGoogle Scholar
De Graaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Falco, R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids 20 (10), S124–S132.CrossRefGoogle Scholar
Fulachier, L. & Dumas, R. 1976 Spectral analogy between temperature and velocity fluctuations in a turbulent boundary layer. J. Fluid Mech. 77 (2), 257–277.CrossRefGoogle Scholar
Gibson, C. H., Friehe, C. A. & McConnell, S. O. 1977 Structure of sheared turbulent fields. Phys. Fluids 20 (10), S156–S167.CrossRefGoogle Scholar
Gladstone, J. H. & Dale, T. P. 1862 Researches on the refraction, dispersion, and sensitiveness of liquids. Proc. R. Soc. Lond. 12, 448–453.Google Scholar
Gordeyev, S., Cress, J. A., Smith, A. E. & Jumper, E. J. 2015 Aero-optical measurements in a subsonic, turbulent boundary layer with non-adiabatic walls. Phys. Fluids 27 (4), 045110.CrossRefGoogle Scholar
Gordeyev, S., Hayden, T. E. & Jumper, E. J. 2007 Aero-optical and flow measurements over a flat-windowed turret. AIAA J. 45 (2), 347–357.CrossRefGoogle Scholar
Gordeyev, S., Jumper, E. J., Ng, T. T. & Cain, A. B.2003 Aero-optical characteristics of compressible, subsonic turbulent boundary layers. AIAA Paper 2003-3606.Google Scholar
Gordeyev, S. & Smith, A. E.2016 Studies of the large-scale structure in turbulent boundary layers using simultaneous velocity-wavefront measurements. AIAA Paper 2016-3804.CrossRefGoogle Scholar
Gordeyev, S., Smith, A. E., Cress, J. A. & Jumper, E. J. 2014 Experimental studies of aero-optical properties of subsonic turbulent boundary layers. J. Fluid Mech. 740, 214–253.CrossRefGoogle Scholar
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
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297–338.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647–664.CrossRefGoogle ScholarPubMed
Jumper, E. J. & Gordeyev, S. 2017 Physics and measurement of aero-optical effects: past and present. Annu. Rev. Fluid Mech. 49 (1), 419–441.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1989 Transport of passive scalars in a turbulent channel flow. In Turbulent Shear Flows 6, pp. 85–96. Springer.CrossRefGoogle 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 (11), 4163–4176.CrossRefGoogle Scholar
Li, Q., Schlatter, P., Brandt, L. & Henningson, D. S. 2009 DNS of a spatially developing turbulent boundary layer with passive scalar transport. Intl J. Heat Fluid Flow 30 (5), 916–929.CrossRefGoogle Scholar
Lozano-Duran, A., Flores, O. & Jimenez, J. 2012 The three-dimensional structure of momentum transfer in turbulent channels. J. Fluid Mech. 694, 100–130.CrossRefGoogle Scholar
Malley, M. M., Sutton, G. W. & Kincheloe, N. 1992 Beam-jitter measurements of turbulent aero-optical path differences. Appl. Opt. 31, 4440–4443.CrossRefGoogle ScholarPubMed
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.CrossRefGoogle Scholar
McKeon, B. J. 2017 The engine behind (wall) turbulence: perspectives on scale interactions. J. Fluid Mech. 817, P1.CrossRefGoogle Scholar
Mestayer, P. G., Gibson, C. H., Coantic, M. F. & Patel, A. S. 1976 Local anisotropy in heated and cooled turbulent boundary layers. Phys. Fluids 19 (9), 1279–1287.CrossRefGoogle Scholar
Morkovin, M. V. 1962 Effects of compressibility on turbulent flows. In Mechanique de la Turbulence (ed. Favre, A.), pp. 367–380. CNRS.Google Scholar
Saxton-Fox, T.2018 Coherent structures, their interactions, and their effects on passive scalar transport and aero-optic distortion in a turbulent boundary layer. PhD thesis, California Institute of Technology, Pasadena, CA.Google Scholar
Saxton-Fox, T. & McKeon, B. J. 2017 Coherent structures, uniform momentum zones and the streamwise energy spectrum in wall-bounded turbulent flows. J. Fluid Mech. 826, R6.CrossRefGoogle Scholar
Saxton-Fox, T., McKeon, B. J. & Gordeyev, S. 2019 Effect of coherent structures on aero-optic distortion in a turbulent boundary layer. AIAA J. 57 (7), 2828–2839.CrossRefGoogle Scholar
Saxton-Fox, T., McKeon, B. J., Gordeyev, S. & Smith, A. E. 2015 Aero-optical distortion as a marker of turbulent structure. In 11th International Symposium on Particle Image Velocimetry, Santa Barbara, CA.Google Scholar
de Silva, C. M., Kevin, K., Baidya, R., Hutchins, N. & Marusic, I. 2018 Large coherence of spanwise velocity in turbulent boundary layers. J. Fluid Mech. 847, 161–185.CrossRefGoogle Scholar
de Silva, C. M., Philip, J., Hutchins, N. & Marusic, I. 2017 Interfaces of uniform momentum zones in turbulent boundary layers. J. Fluid Mech. 820, 451–478.CrossRefGoogle Scholar
Smith, A. E., Gordeyev, S., Saxton-Fox, T. & McKeon, B. J.2014 Subsonic boundary-layer wavefront spectra for a range of Reynolds numbers. AIAA Paper 2014-2491.CrossRefGoogle Scholar
Smits, A. J. & Dussuage, J.-P. 2006 Turbulent Shear Layers in Supersonic Flow. Springer.Google Scholar
Spalding, D. B. 1961 A single formula for the law of the wall. J. Appl. Mech. 28 (3), 455–458.CrossRefGoogle Scholar
Sreenivasan, K. R. 2018 Turbulent mixing: a perspective. Proc. Natl Acad. Sci. USA 116 (37), 18175–18183.CrossRefGoogle ScholarPubMed
Sreenivasan, K. R. & Antonia, R. A. 1977 Skewness of temperature derivatives in turbulent shear flows. Phys. Fluids 20 (12), 1986–1988.CrossRefGoogle Scholar
Subramanian, C. S., Rajagopalan, S., Antonia, R. A. & Chambers, A. J. 1982 Comparison of conditional sampling and averaging techniques in a turbulent boundary layer. J. Fluid Mech. 123, 335–362.CrossRefGoogle Scholar
Theodorsen, T. 1952 Mechanism of turbulence. In Proceedings of the Midwestern Conference on Fluid Mechanics, Ohio State University, Columbus, OH.Google Scholar
Vanderwel, C. & Tavoularis, S. 2016 Scalar dispersion by coherent structures in uniformly sheared flow generated in a water tunnel. J. Turbul. 17 (7), 633–650.CrossRefGoogle Scholar
Wang, K. & Wang, M. 2012 Aero-optics of subsonic turbulent boundary layers. J. Fluid Mech. 696, 122–151.CrossRefGoogle Scholar
Wang, M., Mani, A. & Gordeyev, S. 2012 Physics and computation of aero-optics. Annu. Rev. Fluid Mech. 44 (1), 299–321.CrossRefGoogle Scholar