Generative AI for Synthesizing Spatio-temporal Wall Pressure Fluctuations in Turbulent Boundary Layers*

Wall pressure fluctuations in turbulent boundary layers are key sources of flow-induced noise, vibration, and hydroacoustic effects in underwater vehicles. Accurately predicting frequency/wavenumber spectra of these fluctuations is critical. Existing models based on Lighthill's wave equation or Kraichnan's Poisson equation often depend on empirical data and lack spatiotemporal features. Simulating these fluctuations requires high-resolution, eddy-resolving simulations such as DNS or WMLES, which is costly and impractical for high Reynolds numbers. We propose a generative learning framework using a probabilistic latent diffusion model and conditional neural field to synthesize spatiotemporal wall pressure fluctuations across different adverse pressure gradients in turbulent boundary layers. This framework generates extended trajectories of instantaneous pressure fluctuation fields in an autoregressive manner given sparse sensor measurements and far-wall velocity. By comparing root-mean-square values, frequency spectra, and wavenumber-frequency spectra of generated spatiotemporal instantaneous pressure fluctuations with DNS reference, we demonstrate the merit and effectiveness of our proposed method.