Eulerian statistically preserved structures in passive scalar advection.

We analyze numerically the time-dependent linear operators that govern the dynamics of Eulerian correlation functions of a decaying passive scalar advected by a stationary, forced two-dimensional Navier-Stokes turbulence. We show how to naturally discuss the dynamics in terms of effective compact operators that display Eulerian statistically preserved structures which determine the anomalous scaling of the correlation functions. In passing we point out a bonus of the present approach, in providing analytic predictions for the time-dependent correlation functions in decaying turbulent transport.