A Computational Study of the Dynamics of the Critical Points in a Simple Fluid Flow

We carry out a computational experiment inspired by a physical experiment by Ouellette and Gollub (PRL 99, 194502 (2007)) where a topological transition of the velocity field in a fluid flow is generated by a grid of magnets. At a well-defined Reynolds number Re the motion of the stagnation points becomes so strong that they may merge and annihilate. Replacing the magnets by a grid of stirrers we obtain the same essential features of the transition, but the resolution allows us to identify two different stages of the process: A range of Re where the annihilation rate of the stagnation points is low but non-zero is followed by a narrow interval where the rate jumps to a high level.