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Open AccessArticle

Reconstruction of Diffusion Coefficients and Power Exponents from Single Lagrangian Trajectories

by Leonid M. Ivanov, Collins A. Collins and Tetyana Margolina

Fluids 2021, 6(3), 111; https://doi.org/10.3390/fluids6030111 - 9 Mar 2021

Cited by 4 | Viewed by 2174

Using discrete wavelets, a novel technique is developed to estimate turbulent diffusion coefficients and power exponents from single Lagrangian particle trajectories. The technique differs from the classical approach (Davis (1991)’s technique) because averaging over a statistical ensemble of the mean square displacement (<X²>) is replaced by averaging along a single Lagrangian trajectory X(t) = {X(t), Y(t)}. Metzler et al. (2014) have demonstrated that for an ergodic (for example, normal diffusion) flow, the mean square displacement is <X²> =

\lim_{T \to \infty} τ_{X}^{2} (T, s)

, where

τ_{X}^{2}

(T, s) = 1/(T − s)

\int_{0}^{T - s} (X (t + Δ t)

− X(t))² dt, T and s are observational and lag times but for weak non-ergodic (such as super-diffusion and sub-diffusion) flows <X²> =

\lim_{T \to \infty} ≪ τ_{X}^{2} (T, s) ≫

, where

≪ \dots ≫

is some additional averaging. Numerical calculations for surface drifters in the Black Sea and isobaric RAFOS floats deployed at mid depths in the California Current system demonstrated that the reconstructed diffusion coefficients were smaller than those calculated by Davis (1991)’s technique. This difference is caused by the choice of the Lagrangian mean. The technique proposed here is applied to the analysis of Lagrangian motions in the Black Sea (horizontal diffusion coefficients varied from 10⁵ to 10⁶ cm²/s) and for the sub-diffusion of two RAFOS floats in the California Current system where power exponents varied from 0.65 to 0.72. RAFOS float motions were found to be strongly non-ergodic and non-Gaussian. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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9 pages, 2598 KB

Open AccessFeature PaperLetter

Lagrangian Drifter to Identify Ocean Eddy Characteristics

by Peter C. Chu and Chenwu Fan

Climate 2019, 7(12), 137; https://doi.org/10.3390/cli7120137 - 5 Dec 2019

Cited by 2 | Viewed by 3494

Abstract

Deterministic–stochastic empirical mode decomposition (EMD) is used to obtain low-frequency (non-diffusive; i.e., background velocity) and high-frequency (diffusive; i.e., eddies) components from a Lagrangian drifter‘s trajectory. Eddy characteristics are determined from the time series of eddy trajectories from individual Lagrangian drifters such as eddy radius, eddy velocity, eddy Rossby number, and the eddy–current kinetic energy ratio. A long-term dataset of the Sound Fixing and Ranging (RAFOS) float time series obtained near the California coast by the Naval Postgraduate School from 1992 to 2004 at depth between 150 and 600 m is used as an example to demonstrate the capability of the deterministic–stochastic EMD. Full article

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