A statistical comparison of finite Time Lyapunov exponents and Okubbo-Weiss parameter

Abstract

In this study, we have investigated stirring and mixing properties of particle transport by analyzing the statistical moments from PDFs of Okubbo-Weiss (OW) or Finite time lyapunov exponet (FTLE) diagnostics. In contrast with OW metric, FTLE tools have the advantage of exploiting both spatial and temporal variability of the velocity field and are in principle able to unveil subgrid filaments generated by chaotic stirring. However, one may wonder whether why this statistical advantage is of practical interest in real-data, mesoscale and sub-mesoscale analysis, because of the uncertainties from resolution and binning of data. Here we have compared the ability of OW and the FTLE statistics in detecting transport and mixing properties in fluid flows. By considering two examples of geophysical interest the meandering jet flow and ABC steady flow, we found that the two approaches provide similar results for slowly evolving vortices at early times. However, the FTLE was also able to predict the filamentary processes. Such filaments were also observed, with some mismatch in the two velocity fields, didn’t show any compact relation with other OW diagnostic. It has been found that the OW is a limiting case of the FTLE, Probability distribution functions (PDFs) of FTLEs and OW are computed to better understand implications for mixing and stirring. The study of the shape of the PDFs and their sensitivity, or lack thereof, to whether the FTLE or OW is computed based on 2D or 3D flows allowed us to make inferences about the nature of mixing and stirring. The probability distribution functions (PDFs) are found to be non Gaussian. The nonGaussianity of these PDFs suggests that parameterization schemes in existing numerical models should be improved.