Reynolds-number evolution of wall-pressure statistics beneath canonical turbulent boundary layers

Abstract

This study investigates the Reynolds-number (Re_\tau) 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_\tau, 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_\tau<11300 in the Melbourne tunnel, atmospheric surface-layer measurements at Re_\tau = O(10^6) and a published simulation dataset at Re_\tau = 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_\tau, 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_\tau