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Deformation of a compliant wall in a turbulent channel flow

Published online by Cambridge University Press:  16 June 2017

Cao Zhang ,
Jin Wang ,
William Blake  and
Joseph Katz Open the ORCID record for Joseph Katz [Opens in a new window]
Cao Zhang
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Jin Wang
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
William Blake
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Joseph Katz*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: katz@jhu.edu
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Abstract

Interaction of a compliant wall with a turbulent channel flow is investigated experimentally by simultaneously measuring the time-resolved, three-dimensional (3D) flow field and the two-dimensional (2D) surface deformation. The optical set-up integrates tomographic particle image velocimetry to measure the flow with Mach–Zehnder interferometry to map the deformation. The Reynolds number is $Re_{\unicode[STIX]{x1D70F}}=2300$, and the Young’s modulus of the wall is 0.93 MPa, resulting in a ratio of shear speed to the centreline velocity ($U_{0}$) of 6.8. The wavenumber–frequency spectra of deformation show the surface motions consist of a non-advected low-frequency component and advected modes, some travelling downstream at approximately $U_{0}$ and others at ${\sim}0.72U_{0}$. The r.m.s. values of the advected and non-advected modes are $0.04~\unicode[STIX]{x03BC}\text{m}$$(0.004\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}})$ and $0.2~\unicode[STIX]{x03BC}\text{m}$ ($0.02\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$), respectively, much smaller than the wall unit ($\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$), hence they do not affect the flow. Trends in the wall dynamics are elucidated by correlating the deformation with flow variables, including the 3D pressure distribution calculated by spatially integrating the material acceleration. Predictions by the Chase [J. Acoust. Soc. Am., vol. 89 (6), pp. 2589–2596] linear model are also calculated and compared to the measured trends. The spatial deformation–pressure correlations peak at $y/h\approx 0.12$ ($h$ is half channel height), the elevation of Reynolds shear stress maximum in the log-layer. Streamwise lagging of the deformation behind the pressure is caused in part by phase lag of the pressure with decreasing distance from the wall, and in part by material damping. Positive deformations (bumps) caused by negative pressure fluctuations are preferentially associated with ejections involving spanwise vortices located downstream and quasi-streamwise vortices with spanwise offset. Results of conditional correlations are consistent with the presence of hairpin-like structures. The negative deformations (dimples) are preferentially associated with positive pressure fluctuations at the transition between an upstream sweep to a downstream ejection.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
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Journal of Fluid Mechanics , Volume 823 , 25 July 2017 , pp. 345 - 390
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© 2017 Cambridge University Press 

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References

Abe, H., Matsuo, Y. & Kawamura, H. 2005 A DNS study of Reynolds-number dependence on pressure fluctuations in a turbulent channel flow. In TSFP Digital Library Online. Begel House Inc.Google 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. & Luxton, R. E. 1971 The response of a turbulent boundary layer to a step change in surface roughness. Part 1. Smooth to rough. J. Fluid Mech. 48, 721–761.CrossRefGoogle Scholar
Atkinson, C., Coudert, S., Foucaut, J.-M., Stanislas, M. & Soria, J. 2011 The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer. Exp. Fluids 50, 1031–1056.CrossRefGoogle Scholar
Atkinson, C. & Soria, J. 2009 An efficient simultaneous reconstruction technique for tomographic particle image velocimetry. Exp. Fluids 47, 553–568.CrossRefGoogle Scholar
Baur, T. & Köngeter, J. 1999 PIV with high temporal resolution for the determination of local pressure reductions from coherent turbulent phenomena. In Proceedings of the 3rd International Workshop on Particle Image Velocimetry, Santa Barbara, USA.Google Scholar
Benjamin, T. B. 1960 Effects of a flexible boundary on hydrodynamic stability. J. Fluid Mech. 9, 513–532.CrossRefGoogle Scholar
Benjamin, T. B. 1963 The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows. J. Fluid Mech. 16, 436–450.CrossRefGoogle Scholar
Bernardini, M., Pirozzoli, S. & Orlandi, P. 2014 Velocity statistics in turbulent channel flow up to Re 𝜏 = 4000. J. Fluid Mech. 742, 171–191.CrossRefGoogle Scholar
Blake, W. K. 1970 Turbulent boundary layer wall pressure fluctuations on smooth and rough walls. J. Fluid Mech. 44, 637–660.CrossRefGoogle Scholar
Blick, E. F. & Walters, R. R. 1968 Turbulent boundary-layer characteristics of compliant surfaces. J. Aircraft 5 (1), 11–16.Google Scholar
Bone, D. J., Bachor, H. A. & Sandeman, R. J. 1986 Fringe-pattern analysis using a 2-D Fourier transform. Appl. Opt. 25 (10), 1653–1660.CrossRefGoogle ScholarPubMed
Bull, M. K. 1967 Wall-pressure fluctuations associated with subsonic turbulent boundary layer flow. J. Fluid Mech. 28 (4), 719–754.CrossRefGoogle Scholar
Bushnell, D. M., Hefner, J. N. & Ash, R. L. 1977 Effect of compliant wall motion on turbulent boundary layers. Phys. Fluids 20, S31–S48.CrossRefGoogle Scholar
Carpenter, P. W. & Garrad, A. D. 1985 The hydrodynamic stability of flows over Kramer-type compliant surfaces. Part 1. Tollmien–Schlichting instabilities. J. Fluid Mech. 155, 465–510.CrossRefGoogle Scholar
Carpenter, P. W. & Garrad, A. D. 1986 The hydrodynamic stability of flows over Kramer-type compliant surfaces. Part 2. Flow-induced surface instabilities. J. Fluid Mech. 170, 199–232.CrossRefGoogle Scholar
Castellini, P., Martarelli, M. & Tomasini, E. P. 2006 Laser Doppler vibrometry: development of advanced solutions answering to technology’s needs. Mech. Syst. Signal Process. 20, 1265–1285.Google Scholar
Chang, P. A., Piomelli, U. & Blake, W. K. 1999 Relationship between wall pressure and velocity field sources. Phys. Fluids 11, 3434–3448.CrossRefGoogle Scholar
Charonko, J. J., King, C. V., Smith, B. L. & Vlachos, P. P. 2010 Assessment of pressure field calculations from particle image velocimetry measurements. Meas. Sci. Technol. 21, 105401.Google Scholar
Chase, D. M. 1991 Generation of fluctuating normal stress in a viscoelastic layer by surface shear stress and pressure as in turbulent boundary-layer flow. J. Acoust. Soc. Am. 89 (6), 2589–2596.CrossRefGoogle Scholar
Choi, H. & Moin, P. 1990 On the spacetime characteristics of wall-pressure fluctuations. Phys. Fluids 2 (8), 1450–1460.CrossRefGoogle Scholar
Choi, K.-S., Yang, X., Clayton, B. R., Glover, E. J., Atlar, M., Semenov, B. N. & Kulik, V. M. 1997 Turbulent drag reduction using compliant surfaces. Proc. R. Soc. Lond. A 453, 2229–2240.Google Scholar
Conte, N. & Jardret, V. 2002 Frequency specific characterization of very soft polymeric materials using nanoindentation testing. Mat. Res. Soc. Symp. Proc. 710, DD7.10.1-6.Google Scholar
Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans. ASME: J. Fluids Engng 100, 215–223.Google Scholar
Dinkelacker, A., Hessel, M., Meier, G. E. A. & Schewe, G. 1977 Investigation of pressure fluctuations beneath a turbulent boundary layer by means of an optical method. Phys. Fluids 20 (10), S216–S224.CrossRefGoogle Scholar
Du, P., Cheng, C., Lu, H. & Zhang, X. 2013 Investigation of cellular contraction forces in the frequency domain using a PDMS micropillar-based force transducer. J. Microelectromech. Syst. 22 (1), 44–53.Google Scholar
Duncan, J. H. 1986 The response of an incompressible viscoelastic coating to pressure fluctuations in a turbulent boundary layer. J. Fluid Mech. 171, 339–363.CrossRefGoogle Scholar
Duncan, J. H., Waxman, A. M. & Tulin, M. P. 1985 The dynamics of waves at the interface between a viscoelastic coating and a fluid flow. J. Fluid Mech. 158, 177.Google Scholar
Elsinga, G. E., Scarano, F., Wieneke, B. & van Oudheusden, B. W. 2006 Tomographic particle image velocimetry. Exp. Fluids 41, 933–947.CrossRefGoogle Scholar
Endo, T. & Himeno, R. 2002 Direct numerical simulation of turbulent flow over a compliant surface. J. Turbul. 3, 1–10.Google Scholar
Ferry, J. D. 1970 Viscoelastic Properties of Polymers. Wiley.Google Scholar
Fisher, D. H. & Blick, E. F. 1966 Turbulent damping by flabby skins. J. Aircraft 3 (2), 163–164.CrossRefGoogle Scholar
Fitzgerald, E. R. & Fitzgerald, J. W. 1998 Blubber and compliant coatings for drag reduction in fluids: V. Driving point shear impedance measurements on compliant surfaces. In Proceedings of International Symp. on Seawater Drag Reduction 22–23 July, Newport, RI, USA (ed. Meng, J. C. S.), pp. 215–218.Google Scholar
Foucaut, J. M., Carlier, J. & Stanislas, M. 2004 PIV optimization for the study of turbulent flow using spectral analysis. Meas. Sci. Technol. 15, 1046–1058.CrossRefGoogle Scholar
Fung, Y. C. 1965 Foundations of Solid Mechanics. Prentice Hall.Google Scholar
Gad-el-Hak, M. 1986 The response of elastic and viscoelastic surfaces to a turbulent boundary layer. Trans. ASME J. Appl. Mech. 53, 206–212.CrossRefGoogle Scholar
Gad-el-Hak, M. 1998 Compliant coatings: the simpler alternative. Exp. Therm. Fluid Sci. 16, 141–156.CrossRefGoogle Scholar
Gad-el-Hak, M. 2002 Compliant coatings for drag reduction. Prog. Aerosp. Sci. 38, 77–99.Google Scholar
Gad-el-Hak, M., Blackwelder, R. F. & Riley, J. J. 1984 On the interaction of compliant coatings with boundary layer flows. J. Fluid Mech. 140, 257–280.Google Scholar
Ganapathisubramani, B., Hutchins, N., Monty, J. P., Chung, D. & Marusic, I. 2012 Amplitude and frequency modulation in wall turbulence. J. Fluid Mech. 712, 61–91.Google Scholar
Ghaemi, S., Ragni, D. & Scarano, F. 2012 PIV-based pressure fluctuations in the turbulent boundary layer. Exp. Fluids 53 (6), 1823–1840.CrossRefGoogle Scholar
Ghaemi, S. & Scarano, F. 2013 Turbulent structure of high-amplitude pressure peaks within the turbulent boundary layer. J. Fluid Mech. 735, 381–426.Google Scholar
Ghiglia, D. C., Mastin, G. A. & Romero, L. A. 1987 Cellular-automata method for phase unwrapping. J. Opt. Soc. Am. A 4 (1), 267–280.CrossRefGoogle Scholar
Ghiglia, D. C. & Pritt, M. D. 1998 Two-Dimensional Phase Unwrapping. Wiley.Google Scholar
Goldstein, R. M., Zebker, H. A. & Werner, C. L. 1988 Satellite radar interferometry: two-dimensional phase unwrapping. Radio Sci. 23 (4), 713–720.CrossRefGoogle Scholar
Graham, J., Kanov, K., Yang, X. I. A., Lee, M. K., Malaya, N., Lalescu, C. C., Burns, R., Eyink, G., Szalay, A., Moser, R. D. & Meneveau, C. 2016 A web services-accessible database of turbulent channel flow and its use for testing a new integral wall model for LES. J. Turbul. 17 (2), 181–215.CrossRefGoogle Scholar
Gurka, R., Liberzon, A., Hefetz, D., Rubinstein, D. & Shavit, U. 1999 Computation of pressure distribution using PIV velocity data. In Proceedings of the 3rd International Workshop on Particle Image Velocimetry, Santa Barbara, USA.Google Scholar
Hansen, R. J. & Hunston, D. L. 1974 An experimental study of turbulent flows over compliant surfaces. J. Sound Vib. 34, 297–308.Google Scholar
Hansen, R. J. & Hunston, D. L. 1983 Fluid-property effects on flow-generated waves on a compliant surface. J. Fluid Mech. 133, 161–177.CrossRefGoogle Scholar
Hansen, R. J., Hunston, D. L., Ni, C. C. & Reischman, M. M. 1980 An experimental study of flow-generated waves on a flexible surface. J. Sound Vib. 68, 317–334.Google Scholar
Harris, G. L. & Lissaman, P. B. S. 1969 Turbulent skin friction on compliant surfaces. AIAA J. 7 (8), 1625–1627.Google Scholar
Hecht, E. 2002 Optics, 4th edn. Addison-Wesley.Google Scholar
Hess, D. E., Peattie, R. A. & Schwarz, W. H. 1993 A noninvasive method for the measurement of flow-induced surface displacement of a compliant surface. Exp. Fluids 14, 78–84.Google Scholar
Hong, J., Katz, J., Meneveau, C. & Schultz, M. P. 2012 Coherent structures and associated subgrid-scale energy transfer in a rough-wall turbulent channel flow. J. Fluid Mech. 712, 92–128.CrossRefGoogle Scholar
Hong, J., Katz, J. & Schultz, M. P. 2011 Near-wall turbulence statistics and flow structures over three-dimensional roughness in a turbulent channel flow. J. Fluid Mech. 667, 1–37.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.CrossRefGoogle Scholar
Hultmark, M. 2012 A theory for the streamwise turbulent fluctuations in high Reynolds number pipe flow. J. Fluid Mech. 707, 575–584.Google Scholar
Hultmark, M., Bailey, S. C. C. & Smits, A. J. 2010 Scaling of near-wall turbulence in pipe flow. J. Fluid Mech. 649, 103–113.Google Scholar
Hutchins, N. & Marusic, I. 2007a Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. 365, 647–664.Google Scholar
Hutchins, N. & Marusic, I. 2007b Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.Google Scholar
Ichioka, Y. & Inuiya, M. 1972 Direct phase detecting system. Appl. Opt. 11 (7), 1507–1514.CrossRefGoogle ScholarPubMed
Itoh, K. 1982 Analysis of the phase unwrapping algorithm. Appl. Opt. 21 (14), 2470.Google Scholar
Jeon, S., Choi, H., Yoo, J. Y. & Moin, P. 1999 Space-time characteristics of the wall shear-stress fluctuations in a low-Reynolds-number channel flow. Phys. Fluids 11 (10), 3084–3094.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.Google Scholar
Joshi, P., Liu, X. & Katz, J. 2014 Effect of mean and fluctuating pressure gradients on boundary layer turbulence. J. Fluid Mech. 748, 36–84.Google Scholar
de Kat, R. & van Oudheusden, B. W. 2010 Instantaneous planar pressure from PIV: analytic and experimental test-cases. In 15th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 5–8.Google Scholar
de Kat, R. & van Oudheusden, B. W. 2012 Instantaneous planar pressure determination from PIV in turbulent flow. Exp. Fluids 52, 1089–1106.Google Scholar
Kim, J. 1983 On the structure of wall bounded turbulent flows. Phys. Fluids 26, 2088–2097.Google Scholar
Kim, J. 1989 On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 205, 421–451.CrossRefGoogle Scholar
Kim, E. & Choi, H. 2014 Space-time characteristics of a compliant wall in a turbulent channel flow. J. Fluid Mech. 756, 30–53.Google Scholar
Ko, S. H. & Schloemer, H. H. 1989 Calculations of turbulent boundary-layer pressure fluctuations transmitted into a viscoelastic layer. J. Acoust. Soc. Am. 85, 1469–1477.Google Scholar
Kobashi, Y. & Ichijo, M. 1986 Wall pressure and its relation to turbulent structure of a boundary layer. Exp. Fluids 4, 49–55.Google Scholar
Koschatzky, V., Moore, P. D., Westerweel, J., Scarano, F. & Boersma, B. J. 2011 High speed PIV applied to aerodynamic noise investigation. Exp. Fluids 50, 863–876.CrossRefGoogle Scholar
Kramer, M. O. 1957 Boundary-layer stabilization by distributed damping. J. Aero. Sci. 24, 459–460.Google Scholar
Kramer, M. O. 1962 Boundary-layer stabilization by distributed damping. Naval Engrs J. 74 (2), 341–348.CrossRefGoogle Scholar
Kulik, V. M., Semenov, B. N., Boiko, A. V., Seoudi, B. M., Chun, H. H. & Lee, I. 2009 Measurement of dynamic properties of viscoelastic materials. Exp. Mech. 49, 417–425.Google Scholar
Landahl, M. T. 1962 On the stability of a laminar incompressible boundary layer over a flexible surface. J. Fluid Mech. 13, 609–632.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1970 Theory of Elasticity, 2nd edn. Pergamon.Google Scholar
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 5200. J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Lee, T., Fisher, M. & Schwarz, W. H. 1993a Investigation of the stable interaction of a passive compliant surface with a turbulent boundary layer. J. Fluid Mech. 257, 373–401.CrossRefGoogle Scholar
Lee, T., Fisher, M. & Schwarz, W. H. 1993b The measurement of flow-induced surface displacement on a compliant surface by optical holographic interferometry. Exp. Fluids 14, 159–168.CrossRefGoogle Scholar
Lee, T., Fisher, M. & Schwarz, W. H. 1995 Investigation of the effects of a compliant surface on boundary-layer stability. J. Fluid Mech. 288, 37–58.Google Scholar
Li, Y., Perlman, E., Wan, M., Yang, Y., Meneveau, C., Burns, R., Chen, S., Szalay, A. & Eyink, G. L. 2008 A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence. J. Turbul. 9, N31.Google Scholar
Liu, X. & Katz, J. 2006 Instantaneous pressure and material acceleration measurements using a four-exposure PIV system. Exp. Fluids 41, 227–240.CrossRefGoogle Scholar
Liu, X. & Katz, J. 2008 Cavitation phenomena occurring due to interaction of shear layer vortices with the trailing corner of a two-dimensional open cavity. Phys. Fluids 20, 041702.Google Scholar
Liu, X. & Katz, J. 2013 Vortex–corner interactions in a cavity shear layer elucidated by time-resolved measurements of the pressure field. J. Fluid Mech. 728, 417–457.Google Scholar
Liu, X., Moreto, J. R. & Siddle-Mitchell, S.2016 Instantaneous pressure reconstruction from measured pressure gradient using rotating parallel ray method. In 54th AIAA Aerospace Sciences Meeting. AIAA SciTech. AIAA 2016-1049.Google Scholar
Liu, Z., Adrian, R. J. & Hanratiy, T. J. 2001 Large-scale modes of turbulent channel flow: transport and structure. J. Fluid Mech. 448, 53–80.CrossRefGoogle Scholar
Lozano-durán, A. & Jiménez, J. 2014 Effect of the computational domain on direct simulations of turbulent channels up to Re 𝜏 = 4200. Phys. Fluids 26 (1), 011702.Google Scholar
Luhar, M., Sharma, A. S. & McKeon, B. J. 2015 A framework for studying the effect of compliant surfaces on wall turbulence. J. Fluid Mech. 768, 415–441.Google Scholar
Mark, J. E.(Ed.) 1999 Polymer Data Handbook. Oxford University Press.Google Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow 31, 418–428.CrossRefGoogle Scholar
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
Mathis, R., Hutchins, N. & Marusic, I. 2011 A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows. J. Fluid Mech. 681, 537–566.Google Scholar
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336–382.Google Scholar
McMichael, J. M., Klebanoff, P. S. & Mease, N. E. 1980 Experimental investigation of drag on a compliant surface. In Viscous Flow Drag Reduction (ed. Hough, G. R.), vol. 72, pp. 410–438. AIAA.Google Scholar
Meinhart, C. D., Wereley, S. T. & Santiago, J. G. 2000 A PIV algorithm for estimating time-averaged velocity fields. Trans. ASME J. Fluids Engng 122, 285–289.Google Scholar
Moffat, R. J. 1988 Describing the uncertainties in experimental results. Exp. Therm. Fluid Sci. 1, 3–17.CrossRefGoogle Scholar
Monty, J. P.2005 Developments in smooth wall turbulent duct flows. PhD thesis, the University of Melbourne.Google Scholar
Naka, Y., Stanislas, M., Foucaut, J., Coudert, S., Laval, J. & Obi, S. 2015 Space-time pressure-velocity correlations in a turbulent boundary layer. J. Fluid Mech. 771, 624–675.Google Scholar
van Oudheusden, B. W. 2013 PIV-based pressure measurement. Meas. Sci. Technol. 24, 032001.Google Scholar
van Oudheusden, B. W., Scarano, F., Roosenboom, E. W. M., Casimiri, E. W. F. & Souverein, L. J. 2007 Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows. Exp. Fluids 43, 153–162.Google Scholar
Perlman, E., Burns, R., Li, Y. & Meneveau, C.2007 Data Exploration of Turbulence Simulations using a Database Cluster. Supercomputing SC07, ACM, IEEE.Google Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Riley, J. J., Gad-el-Hak, M. & Metcalfe, R. W. 1988 Compliant coatings. Annu. Rev. Fluid Mech. 20, 393–420.Google Scholar
Roddier, C. & Roddier, F. 1987 Interferogram analysis using Fourier transform techniques. Appl. Opt. 26 (9), 1668–1673.Google Scholar
Rubino, E. & Loppolo, T. 2016 Young’s modulus and loss tangent measurement of polydimethylsiloxane using an optical lever. J. Polym. Sci. B 54, 747–751.Google Scholar
Salze, E., Bailly, C., Marsden, O. & Juve, D. 2015 Investigation of the wall pressure wavenumber-frequency spectrum beneath a turbulent boundary layer with pressure gradient. In International Symposium on Turbulence and Shear Flow Phenomena, Melbourne, Australia.Google Scholar
Scarano, F. 2013 Tomographic PIV: principles and practice. Meas. Sci. Technol. 24, 012001.Google Scholar
Scharnowski, S., Hain, R. & Kahler, C. J. 2012 Reynolds stress estimation up to single-pixel resolution using PIV-measurements. Exp. Fluids 52, 985–1002.Google Scholar
Schäfer, L., Dierksheide, U., Klaas, M. & Schröder, W. 2011 Investigation of dissipation elements in a fully developed turbulent channel flow by tomographic particle-image velocimetry. Phys. Fluids 23, 035106.Google Scholar
Schrijer, F. F. J. & Scarano, F. 2008 Effect of predictor-corrector filtering on the stability and spatial resolution of iterative PIV interrogation. Exp. Fluids 45, 927–941.Google Scholar
Schröder, A., Geisler, R., Elsinga, G. E., Scarano, F. & Dierksheide, U. 2008 Investigation of a turbulent spot and tripped turbulent boundary layer flow using time-resolved tomographic PIV. Exp. Fluids 44, 305–316.CrossRefGoogle Scholar
Schröder, A., Geisler, R., Staack, K., Elsinga, G. E., Scarano, F., Wieneke, B., Henning, A., Poelma, C. & Westerweel, J. 2011 Eulerian and Lagrangian views of a turbulent boundary layer flow using time-resolved tomographic PIV. Exp. Fluids 50, 1071–1091.CrossRefGoogle Scholar
Schultz, M. P. & Flack, K. A. 2013 Reynolds-number scaling of turbulent channel flow. Phys. Fluids 25, 025104.Google Scholar
Sillero, J. A., Jiménez, J. & Moser, R. D. 2014 Two-point statistics for turbulent boundary layers and channels at Reynolds number up to 𝛿+ ≈ 2000. Phys. Fluids 26, 105109.CrossRefGoogle Scholar
Soria, J. & Willert, C. 2012 On measuring the joint probability density function of three-dimensional velocity components in turbulent flows. Meas. Sci. Technol. 23, 065301.Google Scholar
Tabatabai, H., Oliver, D. E., Rohrbaugh, J. W. & Papadopoulos, C. 2013 Novel applications of laser Doppler vibration measurements to medical imaging. Sens. Imag. 14, 13–28.Google Scholar
Takeda, M., Ina, H. & Kobayashi, S. 1982 Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry. J. Opt. Soc. Am. 72 (1), 156–160.Google Scholar
Talapatra, S. & Katz, J. 2012 Coherent structures in the inner part of a rough wall channel flow resolved using Holographic PIV. J. Fluid Mech. 711, 161–170.Google Scholar
Talapatra, S. & Katz, J. 2013 Three-dimensional velocity measurements in a roughness sublayer using microscopic digital inline holography and optical index matching. Meas. Sci. Technol. 24, 024004.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Tsuji, Y., Fransson, J. H. M., Alfredsson, P. H. & Johansson, A. V. 2007 Pressure statistics and their scaling in high-Reynolds-number turbulent boundary layers. J. Fluid Mech. 585, 1–40.Google Scholar
Tsuji, Y., Imayama, S., Schlatter, P., Alfredsson, P. H., Johansson, A. V., Marusic, I., Hutchins, N. & Monty, J. 2012 Pressure fluctuation in high-Reynolds-number turbulent boundary layer: results from experiments and DNS. J. Turbul. 13 (N50), 1–19.Google Scholar
Wang, Z., Yeo, K. S. & Khoo, B. C. 2006 On two-dimensional linear waves in Blasius boundary layer over viscoelastic layers. Eur. J. Mech. (B/Fluids) 25, 33–58.Google Scholar
Westerweel, J., Geelhoed, P. F. & Lindken, R. 2004 Single-pixel resolution ensemble correlation for micro-PIV applications. Exp. Fluids 37, 375–384.Google Scholar
Wieneke, B. 2008 Volume self-calibration for 3D particle image velocimetry. Exp. Fluids 45, 549–556.Google Scholar
Willmarth, W. W. & Wooldridge, C. E. 1962 Measurements of the fluctuating pressure at the wall beneath a thick turbulent boundary layer. J. Fluid Mech. 14 (2), 187–210.Google Scholar
Wills, J. A. B. 1970 Measurements of the wavenumber/phase velocity spectrum of wall pressure beneath a turbulent boundary layer. J. Fluid Mech. 45 (1), 65–90.CrossRefGoogle Scholar
Worth, N. A., Nickels, T. B. & Swaminathan, N. 2010 A tomographic PIV resolution study based on homogeneous isotropic turbulence DNS data. Exp. Fluids. 49, 637–656.Google Scholar
Wu, Y. & Christensen, K. T. 2010 Spatial structure of a turbulent boundary layer with irregular surface roughness. J. Fluid Mech. 655, 380–418.Google Scholar
Xu, S., Rempfer, D. & Lumley, J. 2003 Turbulence over a compliant surface: numerical simulation and analysis. J. Fluid Mech. 478, 11–34.Google Scholar
Zhang, C., Miorini, R. & Katz, J. 2015 Integrating Mach–Zehnder interferometry with TPIV to measure the time-resolved deformation of a compliant wall along with the 3D velocity field in a turbulent channel flow. Exp. Fluids. 56, 203.Google Scholar

Zhang et al. supplementary movie

Large field of view surface deformation recorded at 2 kHz

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Zhang et al. supplementary movie

Small field of view surface deformation recorded at 3 kHz and low-pass filtered at 25 Hz.

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Zhang et al. supplementary movie

Small field of view surface deformation band-pass pass filtered at 25 Hz

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Small field of view surface deformation high-pass filtered at 67 Hz.

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