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Free Content Relative displacement probability distribution functions from balloons and drifters

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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 −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.

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Document Type: Research Article

Publication date: 2010-05-01

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  • The Journal of Marine Research publishes peer-reviewed research articles covering a broad array of topics in physical, biological and chemical oceanography. Articles that deal with processes, as well as those that report significant observations, are welcome. In the area of biology, studies involving coupling between ecological and physical processes are preferred over those that report systematics. Authors benefit from thorough reviews of their manuscripts, where an attempt is made to maximize clarity. The time between submission and publication is kept to a minimum; there is no page charge.
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