The Geometry of Ocean Mixing
Ana M Mancho
Instituto de Ciencias Matemáticas
Mixing processes in oceans are key contributors to very important features of the current climate. A better understanding of these processes and their representation in climate models is required for improved predictions of climate change [1,2]. Lagrangian tools provide a mathematical description of mixing and transport in fluid flows, since they are used to predict where fluid particles go.
Behind this description underlies Poincaré's idea of seeking geometrical structures over the ocean surface (the phase portrait) that have a role in organizing all trajectories into regions corresponding to qualitatively different types of trajectories. On the figure it is displayed the evaluation of a recently defined Lagrangian tool [3,4] on a velocity field measured from altimetric satellites over the Kuroshio current on selected days in May and June 2003.
On the figure, the organizing centers of this highly aperiodic flow are located at a glance. Also are recognizable phase portraits similar to the cat's eyes of the forced pendulum, or to the forced Duffing equation. The ocean surface resembles a patchwork of interconnected dynamical systems where the complexity of possible particle routes is envisaged.
The computational part of this work was done using the CESGA computer FINIS TERRAE. The authors have been supported by CSIC Grant OCEANTECH No. PIF06-059, Consolider I-MATH C3-0104, MICINN Grants Nos. MTM2008-03754 and MTM2008-03840-E, and the Comunidad de Madrid Project No. SIMUMAT S-0505-ESP-0158.
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 J. A. Jiménez Madrid, A. M. Mancho. Chaos 19 (2009), 013111-1-013111-18.
 C. Mendoza, A.M. Mancho. The hidden geometry of ocean flows. Manuscript in preparation.
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These images have not yet been published, though they are part of a manuscript that is in preparation. Credit: Carolina Mendoza & Ana M Mancho.