Identifying the body force from partial observations of a two-dimensional incompressible velocity field

An algorithm is developed, rigorously justified, and numerically implemented that is capable of determining the full body force used to generate chaotic, turbulent dynamics in two-dimensional Navier-Stokes fluid dynamics. The primary contribution of this result is that the accurate reconstruction of the force requires only partial observation of the state, i.e. sparse observations of the state are sufficient to recover not only the state itself but the unknown forcing function as well even in the fully developed turbulent setting.