Physics-Informed Data Assimilation in Wall-Bounded Turbulence

Data assimilation combines physical models with experimental or numerical data to produce dynamically consistent flow reconstructions. In turbulence, where full resolution is expensive and measurements are sparse, physics-informed data assimilation integrates data with the Navier–Stokes equations to preserve physical realism. Methods such as variational optimisation, ensemble Kalman filters, and physics-informed neural networks (PINNs) enforce conservation laws while fitting observations. The key is to apply the vast amount of physical insights developed in turbulence research to improve the data assimilation techniques which have been developed in the wider scientific communities.

In wall-bounded turbulence—including channel, pipe, and boundary-layer flows—these approaches can recover unmeasured near-wall structures, improve subgrid-scale modelling, and enhance predictive accuracy. Possible project directions include:

1. Reconstructing near-wall velocity fields from sparse pressure or PIV data using data assimilation constrained by wall boundary conditions.
2. Hybrid LES–data assimilation schemes, where wall-stress data are assimilated to correct model drift or to optimise model parameters in large-eddy simulations.
3. Predicting extreme events, such as sudden bursts or high-drag episodes, using assimilated flow fields and physics-informed forecasting models.
4. Optimal sensor placement, identified through adjoint-based sensitivity analysis to improve assimilation efficiency.

By embedding physical laws into data assimilation, these methods bridge the gap between simulation and experiment, offering a pathway to more accurate and interpretable predictions of wall-turbulence dynamics.