Relax, then Punch: Recovering the body force from partial observations of the velocity field.

Using limited observations of the velocity field of the two-dimensional Navier-Stokes equations, we successfully reconstruct the steady body force that drives the flow. The number of observed data points is at least an order of magnitude less than the number of modes that describes the forcing function indicating that the method introduced here is capable of identifying complicated forcing mechanisms from very simple observations. Not only is this method demonstrated on simulations of turbulent 2D Navier-Stokes equations, but we also rigorously justify convergence of the derived algorithm.