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Relative dispersion with finite inertial ranges

Published online by Cambridge University Press:  09 December 2021

J.H. LaCasce Open the ORCID record for J.H. LaCasce [Opens in a new window]  and
Thomas Meunier Open the ORCID record for Thomas Meunier [Opens in a new window]
J.H. LaCasce*
Affiliation:
Department of Geosciences, University of Oslo, 0315 Oslo, Norway
Thomas Meunier
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
*
†Email address for correspondence: [email protected]
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Abstract

Relative dispersion experiments are often analysed using theoretical predictions from two- and three-dimensional turbulence. These apply to infinite inertial ranges, assuming the same dispersive behaviour over all scales. With finite inertial ranges, the metrics are less conclusive. We examine this using pair separation probability density functions (PDFs), obtained by integrating a Fokker–Planck equation with different diffusivity profiles. We consider time-based metrics, such as the relative dispersion, and separation-based metrics, such as the finite scale Lyapunov exponent (FSLE). As the latter cannot be calculated from a PDF, we introduce a new measure, the cumulative inverse separation time (CIST), which can. This behaves like the FSLE, but advantageously has analytical solutions in the inertial ranges. This allows the establishment of consistency between the time- and space-based metrics, something which has been lacking previously. We focus on three dispersion regimes: non-local spreading (as in a two-dimensional enstrophy inertial range), Richardson dispersion (as in an energy inertial range) and diffusion (for uncorrelated pair motion). The time-based metrics are more successful with non-local dispersion, as the corresponding PDF applies from the initial time. Richardson dispersion is barely observed, because the self-similar PDF applies only asymptotically in time. In contrast, the separation-based CIST correctly captures the dependencies, even with a short (one decade) inertial range, and is superior to the traditional FSLE at large scales. Nevertheless, it is advantageous to use all measures together, to seek consistent indications of the dispersion.

JFM classification

Geophysical and Geological Flows: Geostrophic turbulence Mass Transport: Dispersion
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 932 , 10 February 2022 , A39
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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