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Understanding how the surface dynamics of the ocean influence the spawning and larval ecology of many large pelagic species, in particular tuna species, is a major challenge. For temperate tunas, the selection of geographically restricted spawning grounds is influenced by environmental conditions, but the influence of surface mixing properties on the early life stages of these species remains poorly understood. Here, based on ichthyoplankton samples collected over 4 yr and satellite-derived finite size Lyapunov exponents (FSLEs), we examined how horizontal mixing activity drives the probability of presence of Atlantic bluefin tuna Thunnus thynnus larvae. We further analyzed the spatial and temporal scales of the FSLE variability at which the relationship between larval presence and mesoscale activity is maximized. We found that moderate mixing activity strongly favors the spatial-temporal distribution of larval habitats, evidencing an optimal environmental window of bluefin tuna spawning and early life development within the meso scale dynamics. During the spawning season, the Balearic Sea presents a unique spatial and temporal hydrodynamic scenario within the Western Mediterranean. These results can be used for developing oceanographic indicators and improving larval abundance indices that are currently used in Atlantic bluefin tuna stock assessments., This study was funded by the BLUE-FIN TUNA project (SOCIB and IEO joint action), the PANDORA project from the EU2020 Program (Grant Agreement No 773713), and MINECO/FEDER Project MOCCA 256RTI2018-093941-B-C31). I.H.C. acknowledges the Vicenç Mut contract funded by the Government of the Balearic Islands and the European Social Fund (ESF) Operational Programme. The multimission altimeter product was produced by Ssalto/Duacs and provided by CMEMS (http://marine.copernicus.eu).

Trabajo presentado en el Non Linear Processes in Atmospheric and Oceanic flows, celebrado en Madrid, España, del 6 al 8 de julio de 2016

Trabajo presentado en el Non Linear Processes in Atmospheric and Oceanic flows, celebrado en Madrid, España, del 6 al 8 de julio de 2016

Tesis doctoral presentada para optar al título de Doctor en la Universitat de les Illes Balears., Horizontal transport and mixing processes are central to the study of the physical, chemical, and biological dynamics of the ocean. Correct understanding and precise modelling of them are relevant from a theoretical viewpoint and crucial for a range of practical issues, such as plankton dynamics or the fate of pollutant spills. In this regard, the last few years have seen the appearance of interesting new developments on the Lagrangian description of transport and mixing phenomena, many of them coming from the area of nonlinear dynamics. Such approaches do not aim at predicting individual tracer trajectories, but at locating spatial structures that are known from dynamical systems theory to act as templates for the whole flow (Leong and Ottino, 1989; Wiggins, 1992). This is mainly due to the capacity of the Lagrangian diagnostics to exploit the spatiotemporal variability of the velocity field by following fluid particle trajectories, at di erence of Eulerian ones which analyze frozen snapshots of data. Among these Lagrangian techniques, a powerful class consists in the computation of local Lyapunov exponents (LLE) which measure the relative dispersion of transported particles. In particular, there are the so called finite-size Lyapunov exponents (FSLEs) where one computes the time taken by two trajectories, initially separated by a finite distance, to reach a larger final finite distance.

Recent work on Lagrangian descriptors has shown that Finite Time Lyapunov Exponents (FTLE) or Finite Size Lyapunov Exponents (FSLE) can be applied to real or simulated data to characterize the mixing properties and transport barriers of the oceanic flow. However, a more detailed analysis on regional and seasonal variability, and its interpretation, was still lacking. In this paper, we have analyzed the near-surface velocity field derived from the Ocean general circulation model For the Earth Simulator (OFES) using Finite-Size Lyapunov Exponents (FSLE). We have characterized regional and seasonal variability by means of some statistical descriptors. Our results show that horizontal mixing, as measured by FSLEs, is seasonally-varying, attaining its maximum in Summer. FSLEs also strongly vary depending on the region: with our descriptors we have first characterized the mixing properties of Northern and Southern Hemispheres, then the main oceanic basins and ocean currents. We have finally studied the relation between Lagrangian FSLEs and some Eulerian descriptors such as Eddy Kinetic Energy (EKE) and vorticity (w) over the different regions. We have found that Lagrangian and Eulerian descriptors are linked by means of dispersion relations. These relations are useful to characterize the dynamics of different ocean areas, and undoubtedly have an influence on the evolution of biological markers, among other variables., I.H.-C., C.L. and E.H.-G. acknowledge support from MICINN and FEDER through project FISICOS (FIS200760327); A. Turiel has received support from Interreg TOSCA project (G-MED09-425) and Spanish MICINN project MIDAS-6 (AYA2010-22062-C05- 01). The OFES simulation was conducted on the Earth Simulator under the support of JAMSTEC. We thank Earth Simulator Center-JAMSTECH team for providing these data., I.H.-C., C.L. and E.H.-G. acknowledge support from MICINN and FEDER through project FISICOS (FIS200760327); A. Turiel has received support from Interreg TOSCA project (G-MED09-425) and Spanish MICINN project MIDAS-6 (AYA2010-22062-C05-01).

Preprint enviado al 3rd Conference on Nonlinear Science and Complexity, Ankara, July 2010 , Springer (2012), The Lagrangian description of fluid transport has been largely enriched with the introduction of stretching quantifiers such as the different types of Lyapunov exponents. Here we will focus on the finite-size Lyapunov exponent case, as applied to horizontal ocean flows estimated from satellite altimetry. The influence on biological organisms of the structures revealed by the Lyapunov analysis will be illustrated with examples from the bottom and from the top of marine ecosystems: the distribution of phytoplankton in ocean upwelling areas, and the trajectories of frigatebirds in the West Indian Ocean, which fly on top of the ridges of Lyapunov structures. The convenience of moving from a two-dimensional to a fully three-dimensional description is highlighted, IFISC contribution supported by MICINN and FEDER (Spain) trough project FISICOS (FIS200760327).

62 pages, 21 figures, 6 chapters, 3 appendix.-- Presented to The University of Balearic Islands in Partial Fulfillment of the Requirements for the Degree of Master of Science.-- Directors: López, Cristóbal; Hernández-Gracía, Emilio, We have analyzed surface velocity data of the Mediterranean Sea as obtained from a primitive equation circulation model (Diecast model). We have computed the Finite Size Lyapunov Exponents (FSLEs) from this data set, which provide a measure of oceanic horizontal stirring, as well as reveal with their extreme values the barriers of transport. A particular property of the FSLE is that it is able to study spatial structures at scales under the resolution of the velocity data used in this computation. In this way, we can obtain information of submesoscales and mesoscales structures (1-100km). We investigate here how reliable are the results of a Lagrangian diagnosis at a similar and at a finer resolution than that of the velocity data. We address this work by the analysis of two properties: - Multifractal character of the spatial distribution of the FSLE, in order to study its scale invariance properties. - Relative error of the FSLE for three cases: a) by introducing a random perturbation in the velocity data, b) by decreasing the resolution of the velocity field, and finally, c) by adding white noise in the computation of the particle\'s trajectories.

Memoria de tesis doctoral presentada por Verónica Morales Márquez para obtener el título de Doctora en Física por la Universitat de les Illes Balears (UIB), realizada bajo la dirección del Dr. Alejandro Orfila Forster, del Dr. Ismael Hernández Carrasco del Instituto Mediterráneo de Estudios Avanzados (IMEDEA-CSIC) y del Dr. Gonzalo Simarro Grande del Institut de Ciències del Mar (ICM-CSIC)