Optimally coherent sets in geophysical flows: A transfer-operator approach to delimiting the stratospheric polar vortex

Santitissadeekorn, Naratip; Froyland, Gary; Monahan, Adam H.

doi:10.1103/physreve.82.056311

Cited by 47 publications

(35 citation statements)

References 28 publications

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“…The transition matrix approach produced surface maps of 10% greater accuracy than existing oceanographic methods and remains the only approach that enables full three-dimensional mapping. In situations where the underlying dynamics is highly nonstationary, analogous methods have recently been developed [51] and applied both to atmospheric data to map stratospheric vortices [51,52] and to ocean data to track oceanic eddies [53]. In the present setting, we believe that both the conformation and stability interval data are approximately stationary based on earlier findings from Ref.…”

Section: Markov Transition Matrix Analysismentioning

confidence: 79%

Transition dynamics and magic-number-like behavior of frictional granular clusters

et al. 2012

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Force chains, the primary load-bearing structures in dense granular materials, rearrange in response to applied stresses and strains. These self-organized grain columns rely on contacts from weakly stressed grains for lateral support to maintain and find new stable states. However, the dynamics associated with the regulation of the topology of contacts and strong versus weak forces through such contacts remains unclear. This study of local self-organization of frictional particles in a deforming dense granular material exploits a transition matrix to quantify preferred conformations and the most likely conformational transitions. It reveals that favored cluster conformations reside in distinct stability states, reminiscent of "magic numbers" for molecular clusters. To support axial loads, force chains typically reside in more stable states of the stability landscape, preferring stabilizing trusslike, three-cycle contact triangular topologies with neighboring grains. The most likely conformational transitions during force chain failure by buckling correspond to rearrangements among, or loss of, contacts which break the three-cycle topology.

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Section: Markov Transition Matrix Analysismentioning

confidence: 79%

Transition dynamics and magic-number-like behavior of frictional granular clusters

et al. 2012

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“…By applying the flow map to our discrete boxes, we obtain the amount of flow among each pair of nodes, which will be taken as the weight of the corresponding link. More explicitly, the fraction of the fluid that started at node i at time t 0 and ended up at node j after a time τ is given by [9][10][11][12][13][14] :…”

Section: Flow Network Construction From Fluid Motionmentioning

confidence: 99%

Clustering coefficient and periodic orbits in flow networks

Ser‐Giacomi

Hernández-Garcı́a

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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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 also of importance in the context of fluid motion.

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“…Joseph and Legras [30] conclude that high values of FSLE do not correctly identify the vortex boundary, but rather delineate a highly mixing region outside the boundary called the 'stochastic layer'. Other Lagrangian analyses are based on optimally coherent sets [60] and trajectory length [41,14,69]. These methods, however, either lack objectivity (frame-invariance), or identify non-material structures.…”

Section: Introductionmentioning

confidence: 99%

Uncovering the Edge of the Polar Vortex

Serra

Sathe

Beron-Vera

et al. 2017

Journal of the Atmospheric Sciences

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The polar vortices play a crucial role in the formation of the ozone hole and can cause severe weather anomalies. Their boundaries, known as the vortex 'edges', are typically identified via methods that are either frame-dependent or return non-material structures, and hence are unsuitable for assessing material transport barriers. Using two-dimensional velocity data on isentropic surfaces in the northern hemisphere, we show that elliptic Lagrangian Coherent Structures (LCSs) identify the correct outermost material surface dividing the coherent vortex core from the surrounding incoherent surf zone. Despite the purely kinematic construction of LCSs, we find a remarkable contrast in temperature and ozone concentration across the identified vortex boundary. We also show that potential vorticity-based methods, despite their simplicity, misidentify the correct extent of the vortex edge. Finally, exploiting the shrinkage of the vortex at various isentropic levels, we observe a trend in the magnitude of vertical motion inside the vortex which is consistent with previous results.

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Optimally coherent sets in geophysical flows: A transfer-operator approach to delimiting the stratospheric polar vortex

Cited by 47 publications

References 28 publications

Transition dynamics and magic-number-like behavior of frictional granular clusters

Transition dynamics and magic-number-like behavior of frictional granular clusters

Clustering coefficient and periodic orbits in flow networks

Uncovering the Edge of the Polar Vortex

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