Statistical Lagragian characterization of the steady ABC and meandering jet flows.

Abstract

In this study, we carried out a statistical Lagrangian characterization of the steady ABC and Meandering jet flows. The ABC flow is a three-dimensional velocity field which gives rise to chaotic trajectories while the Meandering jet flow is a two-dimensional velocity field capable to mimic the meanders of a western boundary current. The two flows are chosen to capture the chaoticity of dynamic flows in both two and three dimensions. The stirring metric used are the Finite Time Lyapunov Exponents (FTLES) and the Finite Size Lyapunov Exponents (FSLEs). Probability distribution functions (PDFs) of FTLEs and FSLEs are calculated and their moments are used to check for similarity and/or discrepancy of the two metrics. The motivation for the study is that both FTLEs and FSLEs are used synonymously in the analysis of the stirring effected by fluid flows with limited information about their similarity. The FTLE and FSLE fields are proxies to passive tracers which are used to track flow with their numerical values representing tracer oncentrations. These two flow diagnostics are considered to be similar and the choice of which one to use depending on the background and scientific community of the user but this presumption is just arbitrary since there is no scientific proof for it. In this study, we found out that the PDFs of both the two dimensional meandering jet flow and the three dimensional ABC flow are consistently non Gaussian. The non Gaussian nature of the PDFs took us to the conclusion that the diffusive parameterization schemes should not be used in numerical weather predictions. It was also found that the PDFs of FTLEs and FSLEs are distinctly different giving differing values of their respective higher order moments. We conclude that FTLEs and FSLEs can be considered similar for only visualization purposes. In studies involving accuracy measurements and quantification of stirring, the two metrics are not synonymous.