Topology counts: Statistics of critical points in experimental, two-dimensional flow*

Points in a flowing fluid where the speed is zero~--- and therefore no streamline can be drawn~--- are known as critical points and have special topological significance. Two types exist in two-dimensional flows: hyperbolic (saddle) points and elliptic (center) points. Approximating two-dimensional flow with an electromagnetically driven, stably stratified solution in a 90~cm x 90~cm tray, we use particle tracking to measure the velocity field and locate the critical points. Our field of view encompasses $\sim$200 critical points per frame, each of which can be tracked like a particle over many frames. We will discuss the resulting spatiotemporal statistics of critical points in two-dimensional flow, focusing in particular on number fluctuations.