The ocean is a complex system because of its movement patterns, which change from thousands of kilometers to the submesoscale. Transport by the surface ocean is an important issue that has become an area of intensive research (see, e.g., Davidson et al., 2009; Hare et al., 2002; Hays et al., 2010; Jordi et al., 2006; Poulain and Hariri, 2013). In addition, processes of mass transport strongly depend on the conditions of the motion of ambient fluids. The fundamental basis for the study of oceanic mixing processes is related to the Eulerian flow field. Because mass transport is a Lagrangian phenomenon, and is associated with coherent structures, it is necessary to use tools for dispersion modeling that are based on Lagrangian quantities. The Lagrangian approach plays an important role in many practical areas, including: the management of water quality; plans for the discharge of pollutants; the tracking of sediments near rivermouths or stream mouths; the prevention of rivermouth clogging; the provision of detailed predictions for the evolution of different scenarios of intervention for exceptional phenomena, such as oil spills; the management of water recycling and discharge within ports; and the management of activities related to the protection of the marine ecosystem, among others.
On the other side, solutions to several important problems in the marine environment require the knowledge of connectivity of from one site to another through the advection of water parcels. Within this general framework, connectivity is usually described as the exchange of individuals between marine populations. In general, connectivity is modeled using classical advection-diffusion formalism (Roughgarden et al., 1988; Gaines et al., 2003; Siegel et al., 2003; Largier, 2003) and has been applied for many purposes such as assessing pollutant concentrations from the source to other regions, for water quality management, for planning pollutant releases to coastal or offshore waters, for assessing oil spill evolutions, or for managing activities related to the protection of the marine ecosystem (Mitarai et al., 2009; Fischer et al., 1979; Grant et al., 2005). It is important for marine ecosystem science and management to understand, for instance, the persistence of isolated populations and the circulation of genetic information (Treml et al., 2008; Roughgarden et al. 1988; Gaylord and Gaines 2000; James et al. 2002 Palumbi 2003; Trakhtenbrot et al. 2005). Moreover, spatial and temporal patterns of marine organism distribution are greatly influenced by differences or changes in population connectivity (Treml et al., 2008; Levin 1992; Warner 1997).
In the Northern Atlantic, we investigate the connectivity properties between different ocean stations through the application of a Lagrangian approach. A three-dimensional simulation of numerical trajectories was used for this purpose. Additionally, a general comparison was made between the trajectory connections simulated by high resolution and coarse resolution grid velocity fields, as well as two-dimensional observations for different depths. Our findings show that the movement characteristics between stations are affected by many parameters such as meso and submeso scale eddies in the different layers of the basin, which can be generated by winds, internal waves, etc. The effects of mesoscales eddies on the transit times have been clearly distinguished for all areas of the basin, considering that the mentioned eddies generated by baroclinic instabilities, as well as mixing drive by wind and buoyancy, play an important role on the movement and transport of particles in the surface and subsurface layers (Mixed Layer Depth and Barrier Layer Thickness). Results indicate that in mentioned condition, due to coherent vortices and other structures such as filaments and spirals, numerical particles need a longer time to reach final destinations especially around the jets on the western side of the basin.
In the following, as another application of Lagrangian approach we report on the mixing structures and transport properties of the Adriatic Sea surface, as a semi-enclosed basin of the Mediterranean Sea, from October 2006 until December 2011. We examine the dispersion properties of numerical pair particles, through the calculation of time-averaged finite-size Lyapunov exponents (FSLEs), representing a Lagrangian technique for detecting hyperbolic Lagrangian coherent structures (LCSs), in the Adriatic during selected months in each year. The results show the significant effects of river runoff and wind forcing, especially the Bora wind field and Sirocco regime, on the mixing activities of numerical pair particles by the generation of vortices, which appear as a tangle of filaments on the FSLE maps. The stretch/compression lines, which contain high values of the FSLEs, work as robust transport barriers, most having been detected along boundary currents on the eastern and western flanks of the Adriatic, particularly during winter. Numerical experiments have indicated that stable flows, with less mixing activity, occur in the northern part of the Adriatic in June and September of each year, while the Southern Adriatic Pit has flows with more seasonal fluctuations and high values of eddy kinetic energy because of the influence of the Sirocco wind and energetic currents entering from the Ionian Sea.