Observability of vortex flows

We study the observability of one and two point vortex flow from one or two Eulerian or Lagrangian observations. By observability we mean the ability to determine the locations and strengths of the vortices from the time history of the observations. An Eulerian observation is a measurement of the velocity of the flow at a fixed point in the domain of the flow. A Lagrangian observation is the measurement of the position of a particle moving with the fluid. To determine observability we introduce the observability and the strong observability rank conditions and compute them for the various flows and observations. We find that vortex flows with Lagrangian observations tend to be more observable then the same flows with Eulerian observations.