  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.
