Irreversibility and self-organization in hydrodynamic echo experiments

We discuss the reversible-irreversible transition in low-Reynolds hydrodynamic systems driven by external cycling actuation. We introduce a set of models with no auto-organization, and show that a sharp crossover is obtained between a Lyapunov regime in which any noise source, such as thermal noise, is amplified exponentially, and a diffusive regime where this no longer holds. In the latter regime, groups of particles are seen to move cooperatively, yet no spatial organization occurs.