Reynolds-number evolution of wall-pressure statistics beneath canonical turbulent boundary layers
Abstract
This study investigates the Reynolds-number (Re_τ) evolution of wall-pressure statistics beneath zero-pressure-gradient TBLs, and links their logarithmic variation to the increasingly energetic large-scale motions in the logarithmic region. The wall-pressure skewness is found to become more negative with increasing Re_τ, owing to increasing contributions from large-scale wall-pressure fluctuations (that are negatively skewed) and their nonlinear interaction with the statistically invariant inner-scale fluctuations (that are positively skewed). The analysis draws on new, well-resolved simultaneous measurements of wall pressure and streamwise velocity spanning 5000 < Re_τ< 11300 in the Melbourne tunnel, atmospheric surface-layer measurements at Re_τ= O(10^6) and a published simulation dataset at Re_τ= O(10^3). Particular attention is paid to the principal experimental limitations affecting wall-pressure statistics: spatial resolution, Helmholtz resonance, facility noise and statistical convergence. Helmholtz resonance is shown to contaminate inner-scale wall-pressure contributions even after conventional corrections, and reliable estimation of skewness is found to require acquisition durations of O(10^5) eddy-turnover times or longer. The inner-scaled wall pressure spectrum is Reynolds-number invariant over the small-scale regime, in contrast to turbulent channel and pipe flows, whereas at intermediate and large scales it grows substantially with Re_τ, consistent with these internal flows. Linear and quadratic velocity--wall-pressure coherence link these intermediate- and large-scale contributions to two dynamically distinct coherent structures: the self-similar attached-eddy hierarchy and turbulent superstructures, respectively. These analyses establish the connection between the inertial region and the log variation of wall-pressure variance and skewness with Re_τ
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BibTeX
@misc{deshpande2026reynoldsnumber,
title = {{Reynolds-number evolution of wall-pressure statistics beneath canonical turbulent boundary layers}},
author = {Rahul Deshpande and Balaraman Panneerselvam and Vijaya R. R. Gudla and Joe Klewicki and Ivan Marusic},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02121},
eprint = {2609.02121},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02121},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Reynolds-number evolution of wall-pressure statistics beneath canonical turbulent boundary layers
AU - Rahul Deshpande
AU - Balaraman Panneerselvam
AU - Vijaya R. R. Gudla
AU - Joe Klewicki
AU - Ivan Marusic
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02121
UR - https://arxiv.org/abs/2609.02121
AB - This study investigates the Reynolds-number (Re_τ) evolution of wall-pressure statistics beneath zero-pressure-gradient TBLs, and links their logarithmic variation to the increasingly energetic large-scale motions in the logarithmic region. The wall-pressure skewness is found to become more negative with increasing Re_τ, owing to increasing contributions from large-scale wall-pressure fluctuations (that are negatively skewed) and their nonlinear interaction with the statistically invariant inner-scale fluctuations (that are positively skewed). The analysis draws on new, well-resolved simultaneous measurements of wall pressure and streamwise velocity spanning 5000 < Re_τ< 11300 in the Melbourne tunnel, atmospheric surface-layer measurements at Re_τ= O(10^6) and a published simulation dataset at Re_τ= O(10^3). Particular attention is paid to the principal experimental limitations affecting wall-pressure statistics: spatial resolution, Helmholtz resonance, facility noise and statistical convergence. Helmholtz resonance is shown to contaminate inner-scale wall-pressure contributions even after conventional corrections, and reliable estimation of skewness is found to require acquisition durations of O(10^5) eddy-turnover times or longer. The inner-scaled wall pressure spectrum is Reynolds-number invariant over the small-scale regime, in contrast to turbulent channel and pipe flows, whereas at intermediate and large scales it grows substantially with Re_τ, consistent with these internal flows. Linear and quadratic velocity--wall-pressure coherence link these intermediate- and large-scale contributions to two dynamically distinct coherent structures: the self-similar attached-eddy hierarchy and turbulent superstructures, respectively. These analyses establish the connection between the inertial region and the log variation of wall-pressure variance and skewness with Re_τ
ER -