[1] We characterize horizontal mixing and transport structures in the surface circulation of the Mediterranean Sea, as obtained from a primitive equation circulation model. We calculate the Finite Size Lyapunov Exponents (FSLEs) of the velocity data set, which give a direct measure of the local stirring. By proper election of the FSLE parameters, we focus on the mesoscale structures, locating a number of vortices embedded in an intricate network of high-stretching lines. These lines control transport in the system. At the edge of the vortices, a dense tangle of line intersections appears, identifying strong mixing. The spatial distribution of FSLEs, averaged over one year, allows to classify areas in the Mediterranean basin according by their mixing activity. The space average of FSLEs on selected geographical regions gives a measure for quantifying and comparing the mixing seasonal variability. INDEX TERMS: 4568

Oceanic dispersal and connectivity have been identified as crucial factors for structuring marine populations and designing marine protected areas (MPAs). Focusing on larval dispersal by ocean currents, we propose an approach coupling Lagrangian transport and new tools from Network Theory to characterize marine connectivity in the Mediterranean basin. Larvae of different pelagic durations and seasons are modeled as passive tracers advected in a simulated oceanic surface flow from which a network of connected areas is constructed. Hydrodynamical provinces extracted from this network are delimited by frontiers which match multiscale oceanographic features. By examining the repeated occurrence of such boundaries, we identify the spatial scales and geographic structures that would control larval dispersal across the entire seascape. Based on these hydrodynamical units, we study novel connectivity metrics for existing reserves. Our results are discussed in the context of ocean biogeography and MPAs design, having ecological and managerial implications.

We represent transport between different regions of a fluid domain by flow networks, constructed from the discrete representation of the Perron-Frobenius or transfer operator associated to the fluid advection dynamics. The procedure is useful to analyze fluid dynamics in geophysical contexts, as illustrated by the construction of a flow network associated to the surface circulation in the Mediterranean sea. We use network-theory tools to analyze the flow network and gain insights into transport processes. In particular, we quantitatively relate dispersion and mixing characteristics, classically quantified by Lyapunov exponents, to the degree of the network nodes. A family of network entropies is defined from the network adjacency matrix and related to the statistics of stretching in the fluid, in particular, to the Lyapunov exponent field. Finally, we use a network community detection algorithm, Infomap, to partition the Mediterranean network into coherent regions, i.e., areas internally well mixed, but with little fluid interchange between them. Water and air transport are among the basic processes shaping the climate of our planet. Heat and salinity fluxes change sea water density and thus drive the global thermohaline circulation. Atmospheric winds force the ocean motion, and also transport moisture, heat or chemicals, impacting the regional climate. These considerations of geophysical fluid motion suggests viewing fluid transport as a transportation network in which fluid advances along different branches that eventually split and merge. In this paper, we exploit this interpretation of fluid transport as a flow network so that we can use the powerful techniques of modern network theory to better characterize transport, mixing, and dispersion, with examples from ocean flows.

We introduce a simple model of population dynamics which considers reproducing individuals or particles with birth and death rates depending on the number of other individuals in their neighborhood. The model shows an inhomogeneous quasistationary pattern with many different clusters of particles arranged periodically in space. We derive the equation for the macroscopic density of particles, perform a linear stability analysis on it, and show that there is a finite-wavelength instability leading to pattern formation. This is responsible for the approximate periodicity with which the clusters of particles arrange in the microscopic model. In addition, we consider the population when immersed in a fluid medium and analyze the influence of advection on global properties of the model, such as the average number of individuals.