Characteristics of anomalous deterministic transport in steady plane viscous flows

We consider transport of passive particles in steady laminar plane flows of incompressible viscous fluids. While drifting along the streamlines, the particles experience alternating accelerations and slowdowns. For an ensemble of particles, recurring slow passages across the vicinities of stagnation points affect the transport and result in the unbounded growth of the ensemble variance. This growth is logarithmic in case of generic stagnation points and has a power-law character in the presence of degeneracies. We interrelate quantitative characteristics of the variance growth with the singularities of the passage time and derive explicit estimates for the transport exponents.