Spectral-clustering approach to Lagrangian vortex detection.
TLDR
This work locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking and illustrates the performance of this technique by identifying coherent Lagrangian vortice in several two- and three-dimensional flows.Abstract:
One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent Lagrangian vortices in several two- and three-dimensional flows.read more
Citations
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A critical comparison of Lagrangian methods for coherent structure detection
TL;DR: In this paper, the authors review and test twelve different approaches to the detection of finite-time coherent material structures in two-dimensional, temporally aperiodic flows, comparing their performance on three benchmark examples: the quasiperiodically forced Bickley jet, a twodimensional turbulence simulation, and an observational wind velocity field from Jupiter's atmosphere.
Journal ArticleDOI
Coherent structure colouring: identification of coherent structures from sparse data using graph theory
TL;DR: This algorithm is shown to robustly detect coherent structures from Lagrangian flow trajectories using significantly less flow data than are required by existing spectral graph theory methods.
Journal ArticleDOI
Generalized Lagrangian coherent structures
TL;DR: In this article, the concept of Lagrangian Coherent Structure (LCS) is generalized to capture coherence in other quantities of interest that are transported by, but not fully locked to, the fluid.
Journal ArticleDOI
A novel method of low-dimensional representation for temporal behavior of flow fields using deep autoencoder
Noriyasu Omata,Susumu Shirayama +1 more
TL;DR: This paper proposes a data-driven nonlinear low-dimensional representation method for unsteady flow fields that preserves its spatial structure and uses a convolutional autoencoder, which is a deep learning technique.
Journal ArticleDOI
Understanding the geometry of transport: diffusion maps for Lagrangian trajectory data unravel coherent sets
Ralf Banisch,Péter Koltai +1 more
TL;DR: In this article, a method for extracting coherent sets from possibly sparse Lagrangian trajectory data is proposed, which can be seen as an extension of diffusion maps to trajectory space, and it allows us to construct "dynamical coordinates" which reveal the intrinsic low-dimensional organization of the data.
References
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Spectral Graph Theory
TL;DR: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigen values and quasi-randomness