Abstract
The finite size Lyapunov exponent (FSLE) has been used extensively since the late 1990s to diagnose turbulent regimes from Lagrangian experiments and to detect Lagrangian coherent structures in geophysical flows and two-dimensional turbulence. Historically, the FSLE was defined in terms of its computational method rather than via a mathematical formulation, and the behavior of the FSLE in the turbulent inertial ranges is based primarily on scaling arguments. Here, we propose an exact definition of the FSLE based on conditional averaging of the finite amplitude growth rate (FAGR) of the particle pair separation. With this new definition, we show that the FSLE is a close proxy for the inverse structural time, a concept introduced a decade before the FSLE. The (in)dependence of the FSLE on initial conditions is also discussed, as well as the links between the FAGR and other relevant Lagrangian metrics, such as the finite time Lyapunov exponent and the second-order velocity structure function.
Highlights
Lagrangian relative dispersion experiments, consisting in the simultaneous release of large numbers of particle pairs and studying their separation characteristics, are a powerful way to assess turbulent properties of a flow
This measure can be positive or negative. The latter authors dismissed λ(ri ) as a proper proxy for finite size Lyapunov exponent (FSLE) because it is not strictly a separation-based metric, as the relative dispersion involves averaging in time
We propose a rigorous derivation of λ by introducing a new variable: the single-realization finite amplitude growth rate, γ (FAGR)
Summary
Lagrangian relative dispersion experiments, consisting in the simultaneous release of large numbers of particle pairs and studying their separation characteristics, are a powerful way to assess turbulent properties of a flow. If a minimum time is used, the FSLE can saturate, yielding the false impression of exponential growth [3,8,17] This issue is usually avoided by increasing the separation factor, α, or by interpolating the pair separations to smaller time steps [3,9]. This measure can be positive or negative The latter authors dismissed λ(ri ) as a proper proxy for FSLE because it is not strictly a separation-based metric, as the relative dispersion involves averaging in time. Such averaging potentially combines contributions from different dispersive regimes. It is possible to build a mathematical definition of the FSLE using the CVE
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
