Exponential Decay of Chaotically Advected Passive Scalars in the Zero Diffusivity Limit

The time asymptotic decay of the variance of a passive scalar in a chaotic flow is studied. Two mechanisms for this decay, which involve processes at short and long length scales, respectively, are considered. The validity of the short length scale mechanism, which is based on Lagrangian stretching theory, is discussed. We also investigate the regimes of applicability and observable signatures of the two mechanisms. Supporting evidence is provided by high resolution numerical experiments.