2025/07/30 by Massey, Jonathan M. O., Smits, Alexander J., McKeon, Beverley J.
#Data Analysis #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Statistics and Probability (physics.data-an)
paper · doi:10.48550/arxiv.2507.23098
Wall-pressure fluctuations beneath turbulent boundary layers drive noise and structural fatigue through interactions between fluid and structural modes. Conventional predictive models for the spectrum--such as the widely accepted Goody model (AIAA Journal 42 (9), 2004, 1788--1794)--fail to capture the energetic growth in the low-frequency range that occurs at high Reynolds number, while at the same time over-predicting the variance. To address these shortcomings, two semi-empirical models are proposed for the wall-pressure spectrum in canonical turbulent boundary layers, pipes and channels for friction Reynolds numbers δ+ ranging from 180 to 47 000. Consistent with the approach outlined modelling the streamwise Reynolds stress in the recent work of Gustenyov et al. (J. Fluid Mech. 1016, 2025, A23), the models are based on consideration of two eddy populations that broadly represent the contributions to the wall pressure fluctuations from inner-scale motions and outer-scale motions. The first model expresses the pre-multiplied spectrum as the sum of two overlapping log-normal populations: an inner-scaled term that is δ+-invariant and an outer-scaled term whose amplitude broadens smoothly with δ+. The model reproduces the 1-D convective signature and the emergence of an outer-scaled peak at large δ+. The second model, developed around newly available pipe data, uses theoretical arguments to prescribe the spectral shapes of the inner and outer populations. Embedding the δ+-dependence in smooth asymptotic functions yields a formulation that varies continuously with δ+ and generalises beyond the calibration range. Both models capture the full spectrum and recover the observed logarithmic growth of its variance, laying the groundwork for more accurate engineering predictions of wall-pressure fluctuations.