The intriguing fluid-dynamical phenomena that take place during transition to turbulence and in fully turbulent flows are commonly probed by experiments and simulations. Experiments contend with a trade-off between field of view and spatio-temporal resolution as well as the difficulty of directly probing quantities of interest. On the other hand, simulations can explicitly compute any term in the flow equations; but simulations invoke idealizations and modeling assumptions in extreme flow regimes (e.g. high Mach and Reynolds numbers). And no matter the approach, once we step beyond canonical configurations, the scarcity of available observations frustrates both experimental and computational researchers alike.

In order to leverage the strengths of simulations and experiments and also mitigate their respective deficiencies, our group developed the framework of observation-infused simulations. We directly infuse the available and incomplete observations data in the simulations, and we predict the optimal interpretation of the missing content.

The figure above shows an example of under-resolved observations in turbulent channel flow and the outcome of infusing these measurements in our simulation.

- Top panel: The line contours represent the true (unknown) velocity field that is probed, and the colored pixels are the available under-resolved measurements. Our objective is to reconstruct the full flow from just the observations.
- Bottom panel: The color contours show our prediction of the instantaneous velocity field, and they are compared to the lines which are the (unknown) truth.

Our group has developed adjoint- (4DVar) and ensemble- (EnVar) variational techniques to solve these problems as well as machine learning (ML) techniques. We have also developed new techniques to (1) determine the minimum sensor resolution to reconstruct turbulence, (2) optimize the placement of sensors to maximize the accuracy of the flow prediction. Ongoing projects including the following:

- Prediction of upstream disturbances in transitional hypersonic flows from limited observations;
- Reconstruction of remote scalar sources and velocity field in stratified turbulence from scarce measurements;
- Prediction of high-Reynolds-number separated flows from limited observations.