Concepts and tools from network theory, the so-called Lagrangian Flow Network framework, have been successfully used to obtain a coarse-grained description of transport by closed fluid flows. Here we explore the application of this methodology to open chaotic flows, and check it with numerical results for a model open flow, namely a jet with a localized wave perturbation. We find that network nodes with high values of out-degree and of finite-time entropy in the forward-in-time direction identify the location of the chaotic saddle and its stable manifold, whereas nodes with high in-degree and backwards finite-time entropy highlight the location of the saddle and its unstable manifold. The cyclic clustering coefficient, associated to the presence of periodic orbits, takes non-vanishing values at the location of the saddle itself., LAOP, CTM2015-66407-P (AEI/FEDER,EU), ESOTECOS FIS2015-63628-C2-1-R (AEI/FEDER, EU), “Investissements d’Avenir” implemented by ANR
(ANR-10-LABX-54 MEMOLIFE and ANR-11-IDEX-0001-02 PSL Research University), Peer reviewed

We show that the clustering coefficient, a standard measure in network theory, when applied to flow networks, i.e., graph representations of fluid flows in which links between nodes represent fluid transport between spatial regions, identifies approximate locations of periodic trajectories in the flow system. This is true for steady flows and for periodic ones in which the time interval τ used to construct the network is the period of the flow or a multiple of it. In other situations, the clustering coefficient still identifies cyclic motion between regions of the fluid. Besides the fluid context, these ideas apply equally well to general dynamical systems. By varying the value of τ used to construct the network, a kind of spectroscopy can be performed so that the observation of high values of mean clustering at a value of τ reveals the presence of periodic orbits of period 3τ
, which impact phase space significantly. These results are illustrated with examples of increasing complexity, namely, a steady and a periodically perturbed model two-dimensional fluid flow, the three-dimensional Lorenz system, and the turbulent surface flow obtained from a numerical model of circulation in the Mediterranean sea.
The Lagrangian description of fluid dynamics, which focuses on the motion of the fluid particles as they are advected by the flow, provides a useful bridge between the theory of dynamical systems and the analysis of fluid transport and mixing, so that techniques and results can be transferred from one field to the other. Modern network theory has also been brought into contact with fluid dynamics and dynamical systems through the concept of flow networks, in which the motion of fluid particles between different regions is represented by links in a graph. In this paper, we use the flow network framework to show that the clustering coefficient, a standard measure in network theory, identifies periodic orbits, fundamental objects in the theory of dynamical systems, and is also of importance in the context of fluid motion., We acknowledge the financial support from Spanish Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional under grants LAOP, CTM2015-66407-P (MINECO/FEDER) and ESOTECOS projects FIS2015-63628-C2-1-R (MINECO/FEDER), FIS2015-63628-C2-2-R (MINECO/FEDER), and from the program “Investissements d'Avenir” launched by the French Government and implemented by ANR under grants ANR-10-LABX-54 MEMOLIFE and ANR-11-IDEX-0001-02 PSL* Research University., No

A stochastic birth-death competition model for particles with excluded volume is proposed. The particles move, reproduce, and die on a regular lattice. While the death rate is constant, the birth rate is spatially nonlocal and implements inter-particle competition by a dependence on the number of particles within a finite distance. The finite volume of particles is accounted for by fixing an upper value to the number of particles that can occupy a lattice node, compromising births and movements. We derive closed macroscopic equations for the density of particles and spatial correlation at two adjacent sites. Under different conditions, the description is further reduced to a single equation for the particle density that contains three terms: diffusion, a linear death, and a highly nonlinear and nonlocal birth term. Steady-state homogeneous solutions, their stability which reveals spatial pattern formation, and the dynamics of time-dependent homogeneous solutions are discussed and compared, in the one-dimensional case, with numerical simulations of the particle system., We acknowledge financial support from grants LAOP, CTM2015-66407-P (AEI/FEDER, EU) and ESOTECOS, FIS2015-63628-C2-1-R and FIS2015-63628-C2-2-R (AEI/FEDER,
EU)., No

Quantifying the mechanisms of tracer dispersion in the ocean remains a central question in oceanography, for problems ranging from nutrient delivery to phytoplankton, to the early detection of contaminants. Until now, most of the analysis has been based on Lagrangian concepts of transport, often focusing on the identification of features that minimize fluid exchange among regions, or more recently, on network tools which focus instead on connectivity and transport pathways. Neither of these approaches, however, allows us to rank the geographical sites of major water passage, and at the same time, to select them so that they monitor waters coming from separate parts of the ocean. These are instead key criteria when deploying an observing network. Here, we address this issue by estimating at any point the extent of the ocean surface which transits through it in a given time window. With such information we are able to rank the sites with major fluxes that intercept waters originating from different regions. We show that this allows us to optimize an observing network, where a set of sampling sites can be chosen for monitoring the largest flux of water dispersing out of a given region. When the analysis is performed backward in time, this method allows us to identify the major sources which feed a target region. The method is first applied to a minimalistic model of a mesoscale eddy field, and then to realistic satellite-derived ocean currents in the Kerguelen area. In this region, we identify the optimal location of fixed stations capable of intercepting the trajectories of 43 surface drifters, along with statistics on the temporal persistence of the stations determined in this way. We then identify possible hotspots of micro-nutrient enrichment for the recurrent spring phytoplanktonic bloom occurring here. Promising applications to other fields, such as larval connectivity, marine spatial planning or contaminant detection, are then discussed., This work is a contribution to the CNES/TOSCA projects LAECOS and BIOSWOT, and it was partly funded by the Copernicus Marine Environment Monitoring Service (CMEMS) Sea Level Thematic Assembly Centre (SL-TAC). C.L and E. H-G. acknowledge support from Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional through the LAOP project (CTM2015-66407-P, MINECO/FEDER)., No