Fingerprints of random flows?

We consider the patterns formed by small rodlike objects advected by a random flow in two dimensions. An exact solution indicates that their direction field is nonsingular. However, we find from simulations that the direction field of the rods does appear to exhibit singularities. First, “scar lines” emerge where the rods abruptly change direction by π. Later, these scar lines become so narrow that they “heal over” and disappear, but their ends remain as point singularities, which are of the same type as those seen in fingerprints. We give a theoretical explanation for these observations.