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    Time-varying coherence of an attached-eddy wall imprint

    Chulan Hu1 and Xuebo Li2,*

    • *Contact author: xbl@cqut.edu.cn

    Phys. Rev. Fluids 11, 084609 – Published 24 August, 2026

    DOI: https://doi.org/10.1103/c14d-fq3p

    Abstract

    The wall imprint of outer-layer motions in wall turbulence is inherently intermittent, yet most attached-eddy coherence analyses are ensemble averaged. Here we develop a time-resolved coherence framework to track the intermittent wall imprint of logarithmic-region motions, using the near-wall velocity record as an operational wall-signature proxy. The method diagnoses scale-local linear common variance between the near-wall and logarithmic-region velocity records; it does not identify individual eddy boundaries or imply a one-to-one geometrical correspondence between motions at the two heights. Synchronized two-point hot-wire measurements in a high-Reynolds-number, nominally zero-pressure-gradient turbulent boundary layer are analyzed (E2-type Melbourne dataset), with a near-wall reference u(zR,t) and a logarithmic-region signal u(z,t). A time-varying squared linear coherence γL2(t,f) is obtained from wavelet coherence. Upon averaging, the wavelet estimator reproduces the classical coherence behavior: 〈γL2〉t matches short-time Fourier estimates over the energetic band and collapses with established similarity trends when expressed versus λx/Δz. To summarize event persistence, we define a critical streamwise scale λs(t) from the first down-crossing of a windowed autocorrelation of the large-scale component of u(z,t). Across heights, λs¯(z)/δ increases, while γL2(λs(t),t) decreases within the logarithmic region, consistent with a weakening wall imprint with wall-normal separation. We then couple γL2(t,f) to a third-order-increment energy-flux surrogate Π(λx/δ,t) to form coherence-conditioned cascade measures. Conditioning on a strong wall imprint yields a systematic wall-normal dependence: The high-coherence conditional flux weakens with increasing z/δ for λx/δ≲O(1) and approaches zero at the largest scales. Finally, collocated wavelet energy-coherence statistics quantify how outer-layer energy is redistributed across coherence levels and reveal a peak in high-coherence conditional mean energy within the logarithmic region.

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