Lagrangian Flow Networks Research Articles

Lagrangian flow networks for passive dispersal: Tracers versus finite-size particles.

The transport and distribution of organisms such as larvae, seeds, or litter in the ocean as well as particles in industrial flows is often approximated by a transport of tracer particles. We present a theoretical investigation to check the accuracy of this approximation by studying the transport of inertial particles between different islands embedded in an open hydrodynamic flow aiming at the construction of a Lagrangian flow network reflecting the connectivity between the islands. To this end, we formulate a two-dimensional kinematic flow field which allows the placement of an arbitrary number of islands at arbitrary locations in a flow of prescribed direction. To account for the mixing in the flow, we include a von Kármán vortex street in the wake of each island. We demonstrate that the transport probabilities of inertial particles making up the links of the Lagrangian flow network essentially depend on the properties of the particles, i.e., their Stokes number, the properties of the flow, and the geometry of the setup of the islands. We find a strong segregation between aerosols and bubbles. Upon comparing the mobility of inertial particles to that of tracers or neutrally buoyant particles, it becomes apparent that the tracer approximation may not always accurately predict the probability of movement. This can lead to inconsistent forecasts regarding the fate of marine organisms, seeds, litter, or particles in industrial flows.

Qualitative and quantitative analysis of interaction between cavitation patterns and vortices of a pitching hydrofoil from Lagrangian viewpoint

The evolution of transient flow structures and mass transport in cavitating flow around a pitching hydrofoil is investigated qualitatively and quantitatively, and the interaction between cavitation patterns and vortices is elucidated from Lagrangian viewpoint. First, turbulence effects are estimated by the density-corrected k–ω model to account for the local compressibility of the multiphase flow at Reynolds number Re=6.4×105. Then, the formation and evolution of vorticity structures during the whole pitching cycle are analyzed using Lagrangian averaged vorticity deviation method. By comparing the flow structures and hydrodynamic properties at varying angles of attack, the cavitating flow is divided into two distinct stages, namely multi-scale cloud cavitation phase from α+=10° to α−=8°, and traveling sheet cavitation phase from α−=8° to α+=10°. Specifically in cloud cavitation, the formation of the cavitation pattern is closely related to the development of the main vortex. Furthermore, the quantitative analysis method based on Lagrangian flow network is developed to deeply analyze the transport and mixing processes. Importantly, the coherence ratio and the mixing parameter are proposed as transport indicators to precisely quantify the spatial connectivity behavior. Finally, the correlations between vapor fraction, codelength, global coherence ratio and global mixing parameter are evaluated. As the conclusion, it is shown that Lagrangian methods are powerful tool for both qualitative and quantitative analysis, and the results obtained could provide a key and important understanding of the flow structure and changing mechanism between cavitation and vortices in marine hydro and propulsion systems.

Analysis on the dynamic mechanism of Acetes aggregation near a nuclear power cooling water system based on the Lagrangian flow network

The outbreak of nuclear power cooling water system (NPCS) disaster-causing organisms has become more frequent, causing huge economic losses. Therefore, it is necessary to understand the aggregation mechanism of disaster-causing organisms for the risk prevention and control of NPCS. Hence, this study applied the Lagrangian flow network (LFN) to analyze the aggregation mechanism of Acetes near NPCS, as such a complex network can describe the interconnections between massive nodes and has already been used for modeling complex nonlinear systems, revealing how the mechanisms of such novel processes emerge. In this study, the degree and probability paths in the network were used to reveal the transport pathway and aggregation area of Acetes. The experimental results highlighted that the sea area of the nuclear power plant is the key node with a large in-degree of the LFN, where the material easily accumulated. The Acetes near the NPCS mainly originated from the east along two critical paths. Overall, this study demonstrates that the LFN is a feasible approach to predicting the transport and the accumulation of the NPCS disaster-causing plankton.

Mass transport pattern and mechanism in the tide-dominant Bohai Sea

Based on a numerical hydrodynamic model and Lagrangian particle tracking method, the Lagrangian flow network and the Lagrangian residual velocity were derived to exhibit the mass transport pattern in the tide-dominant Bohai Sea. The characteristics of the Lagrangian flow network, represented by degree and hydrodynamic provinces, show distinct regional features in the Central Basin and the three bays. The first-order Lagrangian residual velocity (i.e., the mass transport velocity) can be well maintained over a dozen averaging tidal periods, with its magnitude slightly decreasing with the increasing number of tidal periods. The second-order Lagrangian residual velocity (i.e., the Lagrangian drift velocity) includes the dependence on the initial tidal phase, which is also weakened with the increasing number of tidal periods. The mechanism behind the above two features of the Lagrangian residual velocity is explained theoretically. In the Bohai Sea, with about 15 averaging tidal periods, the Lagrangian residual velocity is approximately independent of the initial tidal phase and close to the mass transport velocity. The streamlines of the Lagrangian residual velocity averaged over 15 tidal periods are parallel to the province boundaries in the Lagrangian flow network, which means that the Lagrangian flow network is determined by the Lagrangian residual current. This may lay the foundation for using Lagrangian flow network to analyze and quantify flow and transport pathways in shallow, tide-dominated coastal regions.

Characteristic signatures of Northern Hemisphere blocking events in a Lagrangian flow network representation of the atmospheric circulation.

In the past few decades, boreal summers have been characterized by an increasing number of extreme weather events in the Northern Hemisphere extratropics, including persistent heat waves, droughts and heavy rainfall events with significant social, economic, and environmental impacts. Many of these events have been associated with the presence of anomalous large-scale atmospheric circulation patterns, in particular, persistent blocking situations, i.e., nearly stationary spatial patterns of air pressure. To contribute to a better understanding of the emergence and dynamical properties of such situations, we construct complex networks representing the atmospheric circulation based on Lagrangian trajectory data of passive tracers advected within the atmospheric flow. For these Lagrangian flow networks, we study the spatial patterns of selected node properties prior to, during, and after different atmospheric blocking events in Northern Hemisphere summer. We highlight the specific network characteristics associated with the sequence of strong blocking episodes over Europe during summer 2010 as an illustrative example. Our results demonstrate the ability of the node degree, entropy, and harmonic closeness centrality based on outgoing links to trace important spatiotemporal characteristics of atmospheric blocking events. In particular, all three measures capture the effective separation of the stationary pressure cell forming the blocking high from the normal westerly flow and the deviation of the main atmospheric currents around it. Our results suggest the utility of further exploiting the Lagrangian flow network approach to atmospheric circulation in future targeted diagnostic and prognostic studies.

Eulerian algorithms for computing some Lagrangian flow network quantities

Originated from the complex network theory, the Lagrangian flow network (LFN) has motivated various tools to analyze fluid flows' transport and mixing behaviors. These tools include the so-called finite time escape rate (FTER), the transition matrix, and also the finite time entropy. This paper proposes novel Eulerian algorithms to compute these LFN quantities in two dimensions based on a partial differential equation (PDE) formulation for the underlying flow map. Compared to the typical Lagrangian computations based on ray tracing, our numerical approaches are computationally efficient. Moreover, for velocity fields obtained numerically by computational fluid dynamic (CFD) solvers, our approach does not require further interpolation of the velocity field but can use the discrete velocity data directly. Finally, we will apply our proposed algorithms to several test examples, including a real-life dataset, to demonstrate the performance of the method.

Analysis of tidal-induced connectivity among coastal regions in the Bohai Sea using the complex network theory

Lagrangian flow network (LFN) with tidal forcing is calculated to unfold the connecting timescale and path among the coastal regions in a weakly nonlinear semi-enclosed sea, called the Bohai Sea (BS), China. By applying the Dijkstra's algorithm, the coastal regions are connected using the minimum connecting time, and the corresponding paths are also revealed. Timescale among the BS coastal regions is mostly less than two years. The connecting time between coastal regions of three bays are asymmetrical due to the hydrodynamic characteristics (e.g., the connecting time of Laizhou Bay coastal regions to Liaodong Bay is the longest, averaging 520 days, averaged connecting time from Liaodong Bay to Laizhou Bay is 458 days; and Bohai Bay needs shorter time to connect the other two bays). There are three crucial pathways and a substantial sub-region to connect coastal regions around the BS (i.e. the pathway across the middle of Liaodong Bay; the pathway across the central basin; the pathway along the Bohai Strait; and the Yellow River Estuary area). Based on the entire BS network, these pathways and sub-region are essential for the construction the LFN in the BS. LFN can serve as a powerful instrument to explore the connectivity and regional exchange of the semi-enclosed sea. Connectivity analysis could provide hydrodynamic reference to support the regional management and systematic planning in the BS.

Ocean Surface Connectivity in the Arctic: Capabilities and Caveats of Community Detection in Lagrangian Flow Networks

AbstractTo identify barriers to transport in a fluid domain, community detection algorithms from network science have been used to divide the domain into clusters that are sparsely connected with each other. In a previous application to the closed domain of the Mediterranean Sea, communities detected by the Infomap algorithm have barriers that often coincide with well‐known oceanographic features. We apply this clustering method to the surface of the Arctic and subarctic oceans and thereby show that it can also be applied to open domains. First, we construct a Lagrangian flow network by simulating the exchange of Lagrangian particles between different bins in an icosahedral‐hexagonal grid. Then, Infomap is applied to identify groups of well‐connected bins. The resolved transport barriers include naturally occurring structures, such as the major currents. As expected, clusters in the Arctic are affected by seasonal and annual variations in sea‐ice concentration. An important caveat of community detection algorithms is that many different divisions into clusters may qualify as good solutions. Moreover, while certain cluster boundaries lie consistently at the same location between different good solutions, other boundary locations vary significantly, making it difficult to assess the physical meaning of a single solution. We therefore consider an ensemble of solutions to find persistent boundaries, trends, and correlations with surface velocities and sea‐ice cover.

Lagrangian Flow Network approach to an open flow model

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.

Introduction to Focus Issue: Complex network perspectives on flow systems.

During the last few years, complex network approaches have demonstrated their great potentials as versatile tools for exploring the structural as well as dynamical properties of dynamical systems from a variety of different fields. Among others, recent successful examples include (i) functional (correlation) network approaches to infer hidden statistical interrelationships between macroscopic regions of the human brain or the Earth's climate system, (ii) Lagrangian flow networks allowing to trace dynamically relevant fluid-flow structures in atmosphere, ocean or, more general, the phase space of complex systems, and (iii) time series networks unveiling fundamental organization principles of dynamical systems. In this spirit, complex network approaches have proven useful for data-driven learning of dynamical processes (like those acting within and between sub-components of the Earth's climate system) that are hidden to other analysis techniques. This Focus Issue presents a collection of contributions addressing the description of flows and associated transport processes from the network point of view and its relationship to other approaches which deal with fluid transport and mixing and/or use complex network techniques.

A perturbation-theoretic approach to Lagrangian flow networks.

Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway, or airline infrastructures over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step. We employ perturbation-theoretic methods to investigate the effects of modifications of transport processes in the underlying flow for three different problem classes: efficient absorption (corresponding to particle trapping or leaking), constant input of particles (with additional source terms modeling, e.g., localized contamination), and shifts of the steady state under probability mass conservation (as arising if the background flow is perturbed itself). Our results demonstrate that in all three cases, changes to the steady state solution can be analytically expressed in terms of the eigensystem of the unperturbed flow and the perturbation itself. These results are potentially relevant for developing more efficient strategies for coping with contaminations of fluid or gaseous media such as ocean and atmosphere by oil spills, radioactive substances, non-reactive chemicals, or volcanic aerosols.

Spatio-temporal organization of dynamics in a two-dimensional periodically driven vortex flow: A Lagrangian flow network perspective.

We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a directed network that describes the exchange of mass between distinct regions of the flow domain. By studying different measures characterizing flow network connectivity at different time-scales, we are able to identify the location of dynamically invariant structures and regions of maximum dispersion. Specifically, our approach allows us to delimit co-existing flow regimes with different dynamics. To validate our findings, we compare several network characteristics to the well-established finite-time Lyapunov exponents and apply a receiver operating characteristic analysis to identify network measures that are particularly useful for unveiling the skeleton of Lagrangian chaos.

Sensitivity and robustness of larval connectivity diagnostics obtained from Lagrangian Flow Networks

Abstract Lagrangian Flow Network (LFN) is a modelling framework in which ocean sub-areas are represented as nodes in a network interconnected by links representing transport of propagules (eggs and larvae) by currents. We asses the sensitivity and robustness of four LFN-derived connectivity metrics measuring retention and exchange. The most relevant parameters are tested over large ranges and a wide region with contrasting hydrodynamics: density of released particles, node size (spatial scale of discretization), Pelagic Larval Duration (PLD) and spawning modality. We find a minimum density of released particles that guarantees reliable values for most of the metrics examined. We also find that node size has a nontrivial influence on them. Connectivity estimates for long PLDs are more robust against biological uncertainties (PLD and spawning date) than for short PLDs. For mass-spawners releasing propagules over short periods (≈ 2-10 days), daily release must be simulated to properly consider connectivity fluctuations due to variable currents. In contrast, average connectivity estimates for species that spawn repeatedly over longer durations (few weeks to few months) remain robust even using longer periodicity (5-10 days). Our results have implications to design connectivity experiments with particle-tracking models and to evaluate the reliability of their results.

Dominant transport pathways in an atmospheric blocking event.

A Lagrangian flow network is constructed for the atmospheric blocking of Eastern Europe and Western Russia in summer 2010. We compute the most probable paths followed by fluid particles, which reveal the Omega-block skeleton of the event. A hierarchy of sets of highly probable paths is introduced to describe transport pathways when the most probable path alone is not representative enough. These sets of paths have the shape of narrow coherent tubes flowing close to the most probable one. Thus, even when the most probable path is not very significant in terms of its probability, it still identifies the geometry of the transport pathways.