Intermittency in passive scalar decay

We consider the decay of a passive scalar in a rough turbulent flow. We show that at large times the scalar intensity is statistically equivalent to the product of two independent random variables. The first factor is a Gaussian variable related to the typical fluctuation at initial conditions. The second factor is essentially the probability that, in a given realization of the flow, tracer particles separate at a very slow rate. Therefore, the large-time scalar distribution is always broader than Gaussian for any initial condition, and large scalar excursions are associated to small relative dispersion events.