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    Convection velocities and velocity coupling of outer-scaled wall-pressure fluctuations in canonical turbulent boundary layers

    Rahul Deshpande1,2,*, Abdelrahman Hassanein3,†, and Woutijn J. Baars3,‡

    • *Contact author: raadeshpande@gmail.com
    • †Contact author: a.h.hassanein@tudelft.nl
    • ‡Contact author: w.j.baars@tudelft.nl

    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 (δ-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 5δ in the streamwise direction (where δ is the boundary layer thickness), which synchronously captures space-time pw data alongside streamwise velocity fluctuations (u) from a single hotwire probe at the array's downstream end. The array is designed to spatially filter pw signals to uncover outer-scale contributions, by accurately resolving the large-scale portion of the frequency-wave-number pw 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 1400≲Reτ≲5200, over which the large-scale energy in the boundary layer grows significantly. This growth is reflected in both the frequency-wave-number pw spectrum and the space-time pw correlations, both of which show scaling trends reflective of the large-scale pressure field convecting at an outer-scaled velocity of 0.75U∞, where U∞ is the freestream velocity. The linear coherence between streamwise velocity and large-scale pw is directly quantified through space-time pw–u correlations, which show increasing magnitudes across the inner region with rising Reτ. 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 pw–u 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-Reτ boundary layers, where large-scale motions increasingly dominate the turbulence dynamics.

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