Persistent patterns in deterministic mixing flows

We present a theoretical approach to the description of persistent passive scalar patterns observed in recent experiments with non-turbulent time-periodic two-dimensional fluid flows. The behaviour of the passive scalar is described in terms of eigenmodes of the evolution operator which coincides with the Frobenius-Perron operator for the corresponding Lagrangian dynamics with small noise; the latter represents the molecular diffusion. The asymptotic behaviour is dominated by the eigenmode with the slowest decay rate, which is shown to be localized in the on-mixing region of the flow.