The focus of relative (pair) dispersion studies in the atmosphere and ocean is often on the mean square particle separation or the Finite Scale Lyapunov Exponent. Much less attention has been paid to the probability density function (PDF) of pair separations, despite that this determines the dispersion. In two-dimensional (2-D), nondivergent, homogeneous flows, the PDF is governed by a Fokker-Planck equation. Analytical solutions exist for the turbulent inertial ranges, but these have rarely been compared to observations.We consider the analytical PDFs for the turbulent inertial ranges and derive a new solution for the 2-D energy range. We then compare the analytical PDFs with those generated with data from three in situ sets: one from a balloon experiment in the stratosphere and two from surface drifter experiments in the ocean. For comparison, we also consider PDFs from a numerical simulation of 2-D turbulence forced at intermediate scales. The results suggest that dispersion at sub-deformation scales is nonlocal, with pair separations growing exponentially in time. This implies the kinetic energy spectra at these scales are at least as steep as κ−3. The dispersion at larger scales is harder to characterize because of the uncertainty in the PDF at larger separations, but the results are consistent with previous inferences. In general the PDF provides useful information on the spreading which can be difficult to discern from the dispersion alone.
LaCasce, J. H.. 2010. "Relative displacement probability distribution functions from balloons and drifters." Journal of Marine Research 68, (3). https://elischolar.library.yale.edu/journal_of_marine_research/274