Data assimilation in high-speed boundary layers using deep operator networks

Transition to turbulence in high-altitude, high-speed flight is often caused by the amplification of boundary-layer instability waves. Recently, estimation of the upstream disturbance spectra from wall-pressure data was performed using ensemble variational (EnVar) data assimilation (Buchta & Zaki, J. Fluid Mech., 916, A44, 2021). The computational cost of EnVar is appreciable because it involves the propagation of an ensemble of solutions, thus requiring many direct numerical simulations (DNS) at each iteration. Deep operator networks (DeepONets) bring new opportunities to accelerate EnVar. DeepONets prediction of the observations can either replace or supplement the DNS in the ensemble propagation step. Performance will be assessed in the context of high-speed boundary layer undergoing transition due to subharmonic resonance of planar and oblique instability waves. Using a combined DeepONets-EnVar algorithm, the dominant frequency and phase difference between 2D and 3D perturbations will be estimated, and the accuracy and efficiency of estimation will be assessed.