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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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Nonlin. Processes Geophys., 22, 663-677, 2015
https://doi.org/10.5194/npg-22-663-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
11 Nov 2015
Local finite-time Lyapunov exponent, local sampling and probabilistic source and destination regions
A. E. BozorgMagham1, S. D. Ross2, and D. G. Schmale III3 1Department of Atmospheric and Oceanic Science, University of Maryland, College Park, MD 20742, USA
2Department of Biomedical Engineering and Mechanics, Virginia Tech, Blacksburg, VA 24061, USA
3Department of Plant Pathology, Physiology, and Weed Science, Virginia Tech, Blacksburg, VA 24061, USA
Abstract. The finite-time Lyapunov exponent (FTLE) is a powerful Lagrangian concept widely used for describing large-scale flow patterns and transport phenomena. However, field experiments usually have modest scales. Therefore, it is necessary to bridge the gap between the concept of FTLE and field experiments. In this paper, two independent observations are discussed: (i) approximation of the local FTLE time series at a fixed location as a function of known distances between the destination (or source) points of released (or collected) particles and local velocity, and (ii) estimation of the distances between the destination (or source) points of the released (or collected) particles when consecutive release (or sampling) events are performed at a fixed location. These two observations lay the groundwork for an ansatz methodology that can practically assist in field experiments where consecutive samples are collected at a fixed location, and it is desirable to attribute source locations to the collected particles, and also in planning of optimal local sampling of passive particles for maximal diversity monitoring of atmospheric assemblages of microorganisms. In addition to deterministic flows, the more realistic case of unresolved turbulence and low-resolution flow data that yield probabilistic source (or destination) regions are studied. It is shown that, similar to deterministic flows, Lagrangian coherent structures (LCS) and local FTLE can describe the separation of probabilistic source (or destination) regions corresponding to consecutively collected (or released) particles.

Citation: BozorgMagham, A. E., Ross, S. D., and Schmale III, D. G.: Local finite-time Lyapunov exponent, local sampling and probabilistic source and destination regions, Nonlin. Processes Geophys., 22, 663-677, https://doi.org/10.5194/npg-22-663-2015, 2015.
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Short summary
In this paper a new interpretation of the local finite-time Lyapunov exponent is proposed. This concept can practically assist in field experiments where samples are collected at a fixed location and it is necessary to attribute long-distance transport phenomena and location of source points to the characteristic variation of the sampled particles. Also, results of this study have the potential to aid in planning of optimal local sampling of passive particles.
In this paper a new interpretation of the local finite-time Lyapunov exponent is proposed. This...
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