Real-time parameter recovery from partial observations.

We modify a standard data assimilation algorithm to 'on-the-fly' recover parameters of a turbulent flow. Four specific examples are highlighted: 1) partial observations of the velocity field in 2D Navier-Stokes simulations allows us to accurately recover the viscosity, 2) partial observations of the state allow us to identify artificial parameters of the Kuramoto-Sivashinsky equation, 3) partial observations of the voriticity field allow for recovery of the Prandtl and Rayleigh numbers in turbulent 2D Rayleigh-Benard convection, and 4) sparse observations of the velocity field allow for a full recovery of the entire forcing field in forced 2D turbulence. The approach highlighted here is significant because the parameter identification is performed as the data is observed, and there is rigorous justification for the algorithm's performance.