NPG Nonlinear Processes in Geophysics NPG Nonlin. Processes Geophys. 1607-7946 Copernicus Publications Göttingen, Germany 10.5194/npg-20-987-2013 Path-integrated Lagrangian measures from the velocity gradient tensor Pérez-Muñuzuri V. https://orcid.org/0000-0001-8316-2299 1 Huhn F. 2 Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain Institute for Mechanical Systems, ETH Zürich, Tannenstrasse 3, 8092 Zürich, Switzerland 15 11 2013 20 6 987 991 Copyright: © 2013 V. Pérez-Muñuzuri 2013 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://npg.copernicus.org/articles/20/987/2013/npg-20-987-2013.html The full text article is available as a PDF file from https://npg.copernicus.org/articles/20/987/2013/npg-20-987-2013.pdf

Spatial maps of the finite-time Lyapunov exponent (FTLE) have been used extensively to study LCS in two-dimensional dynamical systems, in particular with application to transport in unsteady fluid flows. We use the time-periodic double-gyre model to compare spatial fields of FTLE and the path-integrated Eulerian Okubo–Weiss parameter (OW). Both fields correlate strongly, and by solving the dynamics of the deformation gradient tensor, a theoretical relationship between both magnitudes has been obtained. While for long integration times more and more FTLE ridges appear that do not seem to coincide with the stable manifold, ridges in the field of path-integrated OW represent fewer additional structures.

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