Wall Pressure–Velocity Correlations in Turbulent Boundary Layers with Varying Pressure Gradients via a Data-Driven Analysis.

The spatiotemporal correlations between the fluctuating wall pressure and velocity in turbulent boundary layers (TBLs) are examined over a wide range of Reynolds numbers and pressure-gradient conditions to elucidate how coherent turbulence structures influence wall-pressure fluctuations. The analysis leverages our high-fidelity TBL database constructed from incompressible direct numerical simulations, wall-resolved large-eddy simulations, and wall-modeled large-eddy simulations. The dataset spans momentum-thickness Reynolds numbers from 300 to 5000 with seven pressure-gradient conditions for each Reynolds number, resulting in three separated, three attached, and one zero-pressure-gradient (ZPG) TBLs. For the ZPG flows, the pressure-velocity correlations and associated structural signatures agree with established literature. Flow separation significantly enlarges both spatial and temporal correlation scales, while increasing Reynolds number tends to reduce them. To systematically quantify the influence of Reynolds number and pressure gradient, we introduce a data-driven dimensionless learning framework that integrates physical invariance with machine learning to uncover scaling laws governing wall pressure–velocity correlations across diverse flow regimes.