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Convection velocities and velocity coupling of outer-scaled wall-pressure fluctuations in canonical turbulent boundary layers
Phys. Rev. Fluids 11, 064612 – Published 18 June, 2026
DOI: https://doi.org/10.1103/8gn7-k6nm
Abstract
This study shows that the turbulent velocities most strongly correlated with outer-scaled (-scaled) wall-pressure fluctuations beneath a zero-pressure-gradient boundary layer reside within the logarithmic region. Even though contributions from the wake region are present, they are found to be statistically less dominant than those from the logarithmic region. The findings are based on bespoke measurements using an array of 63 microphones spanning in the streamwise direction (where is the boundary layer thickness), which synchronously captures space-time data alongside streamwise velocity fluctuations from a single hotwire probe at the array's downstream end. The array is designed to spatially filter signals to uncover outer-scale contributions, by accurately resolving the large-scale portion of the frequency-wave-number spectrum while avoiding aliasing of small-scale energy. This design, and its effectiveness in anti-aliasing, is validated against previously published low-Reynolds-number simulation datasets of turbulent boundary layer flow. Present experiments span a friction Reynolds number range of , over which the large-scale energy in the boundary layer grows significantly. This growth is reflected in both the frequency-wave-number spectrum and the space-time correlations, both of which show scaling trends reflective of the large-scale pressure field convecting at an outer-scaled velocity of , where is the freestream velocity. The linear coherence between streamwise velocity and large-scale is directly quantified through space-time correlations, which show increasing magnitudes across the inner region with rising . At the top of the logarithmic region, the correlation contours resemble outer-scaled coherent structures akin to large- and very-large-scale motions. A clear Reynolds number trend is also evident in the average convection velocities inferred from correlations, which increasingly deviate from the local mean velocity towards the outer-scaled convection velocity across the inner region. These insights provide a critical foundation for leveraging wall-pressure fluctuations in modeling and control of high- boundary layers, where large-scale motions increasingly dominate the turbulence dynamics.
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References (61)
- W. W. Willmarth, Pressure fluctuations beneath turbulent boundary layers, Annu. Rev. Fluid Mech. 7, 13 (1975).
- S. Lee, L. Ayton, F. Bertagnolio, S. Moreau, T. Chong, and P. Joseph, Turbulent boundary layer trailing-edge noise: Theory, computation, experiment, and application, Prog. Aerosp. Sci. 126, 100737 (2021).
- W. W. Willmarth, Wall pressure fluctuations in a turbulent boundary layer, J. Acoust. Soc. Am. 28, 1048 (1956).
- W. W. Willmarth and C. E. Wooldridge, Measurements of the fluctuating pressure at the wall beneath a thick turbulent boundary layer, J. Fluid Mech. 14, 187 (1962).
- M. K. Bull, Wall-pressure fluctuations associated with subsonic turbulent boundary layer flow, J. Fluid Mech. 28, 719 (1967).
- J. M. Wallace, Space-time correlations in turbulent flow: A review, Theor. Appl. Mech. Lett. 4, 022003 (2014).
- N. A. Balantrapu, W. Nathan Alexander, and W. Devenport, Wall-pressure fluctuations in an axisymmetric boundary layer under strong adverse pressure gradient, J. Fluid Mech. 960, A28 (2023).
- J. A. B. Wills, On convection velocities in turbulent shear flows, J. Fluid Mech. 20, 417 (1964).
- B. M. Abraham and W. L. Keith, Direct measurements of turbulent boundary layer wall pressure wavenumber-frequency spectra, J. Fluids Eng. 120, 29 (1998).
- S. Damani, H. Butt, E. Totten, W. J. Devenport, and T. Lowe, Measurement and analysis of sub-convective wall pressure fluctuations in turbulent boundary layer flows, J. Fluid Mech. 1014, A26 (2025).
- H. Butt, S. Damani, W. Devenport, and T. Lowe, Turbulent boundary layer superstructures and their implications to surface pressure fluctuations, J. Turbul. 26, 399 (2026).
- G. Corcos, The structure of the turbulent pressure field in boundary-layer flows, J. Fluid Mech. 18, 353 (1964).
- D. M. Chase, Modeling the wavevector-frequency spectrum of turbulent boundary layer wall pressure, J. Sound Vib. 70, 29 (1980).
- B. Yang and Z. Yang, On the wavenumber–frequency spectrum of the wall pressure fluctuations in turbulent channel flow, J. Fluid Mech. 937, A39 (2022).
- Y. Tsuji, J. H. M. Fransson, P. H. Alfredsson, and A. V. Johansson, Pressure statistics and their scaling in high-Reynolds-number turbulent boundary layers, J. Fluid Mech. 585, 1 (2007).
- P. A. Chang III, U. Piomelli, and W. K. Blake, Relationship between wall pressure and velocity-field sources, Phys. Fluids 11, 3434 (1999).
- R. L. Panton and J. H. Linebarger, Wall pressure spectra calculations for equilibrium boundary layers, J. Fluid Mech. 65, 261 (1974).
- T. M. Farabee and M. J. Casarella, Spectral features of wall pressure fluctuations beneath turbulent boundary layers, Phys. Fluids 3, 2410 (1991).
- A. E. Perry, S. Henbest, and M. S. Chong, A theoretical and experimental study of wall turbulence, J. Fluid Mech. 165, 163 (1986).
- Y. Naka, M. Stanislas, J.-M. Foucaut, S. Coudert, J.-P. Laval, and S. Obi, Space–time pressure–velocity correlations in a turbulent boundary layer, J. Fluid Mech. 771, 624 (2015).
- B. Gibeau and S. Ghaemi, Low-and mid-frequency wall-pressure sources in a turbulent boundary layer, J. Fluid Mech. 918, A18 (2021).
- I. Marusic, R. Mathis, and N. Hutchins, High Reynolds number effects in wall turbulence, Int. J. Heat Fluid Flow 31, 418 (2010).
- J. C. Klewicki, P. J. A. Priyadarshana, and M. M. Metzger, Statistical structure of the fluctuating wall pressure and its in-plane gradients at high Reynolds number, J. Fluid Mech. 609, 195 (2008).
- W. J. Baars, G. Dacome, and M. Lee, Reynolds-number scaling of wall-pressure–velocity correlations in wall-bounded turbulence, J. Fluid Mech. 981, A15 (2024).
- R. Deshpande, R. Vinuesa, J. Klewicki, and I. Marusic, Active and inactive contributions to the wall pressure and wall-shear stress in turbulent boundary layers, J. Fluid Mech. 1003, A24 (2025).
- G. Schewe, On the structure and resolution of wall-pressure fluctuations associated with turbulent boundary-layer flow, J. Fluid Mech. 134, 311 (1983).
- A. S. W. Thomas and M. K. Bull, On the role of wall-pressure fluctuations in deterministic motions in the turbulent boundary layer, J. Fluid Mech. 128, 283 (1983).
- H. Choi and P. Moin, On the space-time characteristics of wall-pressure fluctuations, Phys. Fluids 2, 1450 (1990).
- S. Anantharamu and K. Mahesh, Analysis of wall-pressure fluctuation sources from direct numerical simulation of turbulent channel flow, J. Fluid Mech. 898, A17 (2020).
- J. C. Del Alamo and J. Jiménez, Estimation of turbulent convection velocities and corrections to Taylor's approximation, J. Fluid Mech. 640, 5 (2009).
- J. LeHew, M. Guala, and B. J. McKeon, A study of the three-dimensional spectral energy distribution in a zero pressure gradient turbulent boundary layer, Exp. Fluids 51, 997 (2011).
- R. de Kat and B. Ganapathisubramani, Frequency–wavenumber mapping in turbulent shear flows, J. Fluid Mech. 783, 166 (2015).
- M. Wilczek, R. J. A. M. Stevens, and C. Meneveau, Spatio-temporal spectra in the logarithmic layer of wall turbulence: Large-eddy simulations and simple models, J. Fluid Mech. 769, R1 (2015).
- D. M. Chase, The character of the turbulent wall pressure spectrum at subconvective wavenumbers and a suggested comprehensive model, J. Sound Vib. 112, 125 (1987).
- M. Luhar, A. S. Sharma, and B. J. McKeon, On the structure and origin of pressure fluctuations in wall turbulence: Predictions based on the resolvent analysis, J. Fluid Mech. 751, 38 (2014).
- A. Agarwal and R. Deshpande, Effects of Reynolds number and spatial resolution on the pressure source terms in turbulent boundary layers, arXiv:2412.19474.
- W. W. Willmarth and C. Wooldridge, Measurements of the correlation between the fluctuating velocities and the fluctuating wall pressure in a thick turbulent boundary layer, Technical Report No. AD0436675 (Advisory Group for Aeronautical Research and Development, Paris, 1963), https://apps.dtic.mil/sti/trecms/pdf/AD0436675.pdf.
- C. Liu and D. F. Gayme, An input–output based analysis of convective velocity in turbulent channels, J. Fluid Mech. 888, A32 (2020).
- G. Dacome, L. Lazzarini, A. Talamelli, G. Bellani, and W. J. Baars, Scaling of wall-pressure–velocity correlations in high Reynolds number turbulent pipe flow, J. Fluid Mech. 1013, A48 (2025).
- S. Pirozzoli and T. Wei, On pressure fluctuations in the near-wall region of turbulent flows, J. Fluid Mech. 1010, A10 (2025).
- M. W. Knoop, A. Hassanein, and W. J. Baars, Development and characterisation of a turbulent boundary layer facility at the Delft University of Technology, Aerosp. Sci. Technol. 168, 110972 (2026).
- N. Hutchins, T. B. Nickels, I. Marusic, and M. Chong, Hot-wire spatial resolution issues in wall-bounded turbulence, J. Fluid Mech. 635, 103 (2009).
- M. Hultmark and A. J. Smits, Temperature corrections for constant temperature and constant current hot-wire anemometers, Meas. Sci. Technol. 21, 105404 (2010).
- K. A. Chauhan, P. A. Monkewitz, and H. M. Nagib, Criteria for assessing experiments in zero pressure gradient boundary layers, Fluid Dyn. Res. 41, 021404 (2009).
- J. A. Sillero, J. Jiménez, and R. D. Moser, One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to 2000, Phys. Fluids 25, 105102 (2013).
- I. Marusic, K. A. Chauhan, V. Kulandaivelu, and N. Hutchins, Evolution of zero-pressure-gradient boundary layers from different tripping conditions, J. Fluid Mech. 783, 379 (2015).
- G. Eitel-Amor, R. Örlü, and P. Schlatter, Simulation and validation of a spatially evolving turbulent boundary layer up to , Int. J. Heat Fluid Flow 47, 57 (2014).
- R. L. Panton, M. Lee, and R. D. Moser, Correlation of pressure fluctuations in turbulent wall layers, Phys. Rev. Fluids 2, 094604 (2017).
- P. Schlatter and R. Örlü, Assessment of direct numerical simulation data of turbulent boundary layers, J. Fluid Mech. 659, 116 (2010).
- C. E. Tinney and P. Jordan, The near pressure field of co-axial subsonic jets, J. Fluid Mech. 611, 175 (2008).
- A. M. Naguib, S. P. Gravante, and C. E. Wark, Extraction of turbulent wall-pressure time-series using an optimal filtering scheme, Exp. Fluids 22, 14 (1996).
- R. Richardson, Y. Zhang, and L. N. Cattafesta, Sensor decontamination via conditional spectral analysis, Exp. Fluids 64, 163 (2023).
- C. M. de Silva, D. Chandran, R. Baidya, N. Hutchins, and I. Marusic, Periodicity of large-scale coherence in turbulent boundary layers, Int. J. Heat Fluid Flow 83, 108575 (2020).
- D. J. Fritsch, V. Vishwanathan, K. Todd Lowe, and W. J. Devenport, Fluctuating pressure beneath smooth wall boundary layers in nonequilibrium pressure gradients, AIAA J. 60, 4725 (2022).
- R. Deshpande, C. M. de Silva, and I. Marusic, Evidence that superstructures comprise self-similar coherent motions in high Reynolds number boundary layers, J. Fluid Mech. 969, A10 (2023).
- W. J. Baars and I. Marusic, Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 1. Energy spectra, J. Fluid Mech. 882, A25 (2020).
- N. Gustenyov, S. Bailey, and A. Smits, A model spectrum for turbulent wall-bounded flow, J. Fluid Mech. 1016, A23 (2025).
- R. Deshpande, C. M. de Silva, M. Lee, J. P. Monty, and I. Marusic, Data-driven enhancement of coherent structure-based models for predicting instantaneous wall turbulence, Int. J. Heat Fluid Flow 92, 108879 (2021).
- J. H. Lee and H. J. Sung, Comparison of very-large-scale motions of turbulent pipe and boundary layer simulations, Phys. Fluids 25, 045103 (2013).
- G. Borrell and J. Jiménez, Properties of the turbulent/non-turbulent interface in boundary layers, J. Fluid Mech. 801, 554 (2016).
- G. Dacome, R. Siebols, and W. J. Baars, Small-scale Helmholtz resonators with grazing turbulent boundary layer flow, J. Turbul. 25, 461 (2024).