  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 less than 10\% of the
number of modes that describes the full flow field, indicating that the method
introduced here is capable of identifying complicated forcing mechanisms from a
relatively small collection of observations. In addition to demonstrating the
efficacy of this method on turbulent flow data generated by simulations of the
two-dimensional Navier-Stokes equations, we also rigorously justify convergence
of the derived algorithm. Beyond the practical applicability of such an
algorithm, the reliance of this method on the dynamical evolution of the system
yields physical insight into the turbulent cascade.
