The asymptotic decay of passive scalar fields is solved analytically for the Kraichnan model, where the velocity has a short correlation time. At long times, two universality classes are found, both characterized by a distribution of the scalar—generally non-Gaussian—with global self-similar evolution in time. Analogous behavior is found numerically with a more realistic flow resulting from an inverse energy cascade.

• Received 5 October 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.2305