Relative dispersion in a single realization of divergent flow

A single realization of time-dependent divergent flow can stir the specific concentration of a passive scalar to coarse-grained spatial uniformity. It is necessary only that the Lagrangian time series of velocity, and of divergence, become independent at sufficiently large separations in time. Independence is defined here in terms of the distributions over the totality of coarse-graining cells that cover the spatial domain. The result applies to two-dimensional flow on isopycnal surfaces in the ocean and the troposphere, and to high speed three-dimensional flow in the stratosphere. The result holds for stationary and moderately nonstationary flow statistics. Homogeneity is not required. The analysis is complicated owing to certain Lagrangian spatial averages not commuting with temporal integrals, but the need to invoke the abstraction of an ensemble of worlds is avoided.