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Transport and mixing in the Mediterranean sea by Finite Size Lyapunov Exponents
Cristóbal López, Francesco d'Ovidio, Emilio Hernández-García and Vicente Fernández
Instituto Mediterráneo de Estudios Avanzados (IMEDEA)
clopez@imedea.uib.es(Abstract received 04/08/2005 for session C)
ABSTRACT
In chlorophyll and temperature patterns taken from satellite pictures one can easily recognise convoluted filaments typical of passive tracers in advection systems. By identifying the surface of the sea with a phase space, one can formally use the velocity field as the definition of a two dimensional, time dependent dynamical system. Then, it is possible to show that the filaments observed are related to unstable manifolds of hyperbolic points. The problem of understanding the observed patterns is thus reconducted to the problem of localizing manifolds in a dynamical system and is of great importance for the marine dynamics, since such manifolds mainly control the transport and mixing properties. Such approach is specially appealing in the last decade, since now models and satellite measurements provide the velocity field with a good spatio-temporal resolution. In this talk I will discuss a technique, the Finite Size Lyapunov Exponents (FSLEs), that allows to locate manifolds of hyperbolic points from a velocity field. I will first discuss the technique on ideal systems, like the von Karman model, and then apply it to both simulation and satellite data of the Mediterranean surface velocity field. I will show that the FSLEs not only predict thermal and chlorophyll patterns, but can also be used to quantify mixing and seasonal oscillations.
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2005 LAPCOD Meeting, Lerici, Italy, June 13-17, 2005