Exploring Continuous Data Assimilation Algorithms for Reconstructing Flow from Temperature Measurements

Many important problems in engineering require reconstructing flow when some state variable observations are unavailable. Inspired by the Charney conjecture, which states that temperature observations are sufficient to recover all other state variables in simple atmospheric models, we explore continuous data assimilation algorithms which use temperature sensor data to reconstruct flow modeled by the Boussinesq equations in turbulent settings with nontrivial geometry. We compare nudging-based approaches with discrete optimization approaches based on minimizing squared residuals of governing equations. We analyze errors and time to convergence in multiple geometric configurations and Rayleigh numbers. Our study sheds new light on the connections between temperature and velocity in combined forced and natural convection problems and demonstrates methods of recovering the full system state using only temperature measurements.