Lyapunov exponents and Lyapunov vectors are precious tools to study dynamical systems: they provide a mathematical framework characterizing sensitive dependence on initial conditions, as well as the stretching and the contraction occurring along a trajectory. Their extension to finite size and finite time calculation has been shown to lead to the location of Coherent Lagrangian Structures, which correspond in geophysical flows to frontal regions. In this case, the Lyapunov exponent and the Lyapunov vector provide, respectively, the cross front gradient amplification and the front orientation. Here we present global maps of Lyapunov exponents/vectors computed from satellite-derived surface currents of the oceans and we quantify their capability of predicting fronts by comparing with Sea Surface Temperature images. We find that in high energetic regions like boundary currents, large relative separations are achieved in short times (few days) and Lyapunov vector mostly align with the direction of jets; in contrast, in lower energetic regions (like the boundaries of subtropical gyres) the Lyapunov calculation allows to predict tracer lobes and filaments generated by the chaotic advection occurring here. These results may be useful for a global calibration and validation of the Lagrangian technique for multidisciplinary oceanographic applications like co-localization of marine animal behaviors to frontal systems and adaptive strategies for biogeochemical field studies.
Beron-Vera FJ, Olascoaga MJ, Goni GJ (2008) Oceanic mesoscale eddies as revealed by Lagrangian coherent structures. Geophys Res Lett 35(12):L12603ADSCrossRefGoogle Scholar
Boffetta G, Lacorata G, Redaelli G, Vulpiani A (2001) Detecting barriers to transport: a review of different techniques. Physica D 159(1–2):58–70ADSCrossRefzbMATHGoogle Scholar
d’Ovidio F, De Monte S, Alvain S, Dandonneau Y, Lévy M (2010) Fluid dynamical niches of phytoplankton types. Proc Natl Acad Sci 107(43):18366–18370ADSCrossRefGoogle Scholar
d’Ovidio F, De Monte S, Della Penna A, Cotté C, Guinet C (2013) Ecological implications of eddy retention in the open ocean: a Lagrangian approach. J Phys A Math Theor 46(25):254023ADSMathSciNetCrossRefzbMATHGoogle Scholar
Lehahn Y, d’Ovidio F, Lévy M, Heifetz E (2007) Stirring of the northeast atlantic spring bloom: a Lagrangian analysis based on multisatellite data. J Geophys Res Oceans 112(C8):C08005ADSCrossRefGoogle Scholar
Shadden SC, Lekien F, Marsden JE (2005) Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 212(3–4):271–304ADSMathSciNetCrossRefzbMATHGoogle Scholar