Network-theoretic approach to sparsified discrete vortex dynamics

We examine discrete vortex dynamics in two-dimensional flow through a network-theoretic approach. The interaction of the vortices is represented with a graph, which allows the use of network-theoretic approaches to identify key vortex-to-vortex interactions. We employ sparsification techniques on th...

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Bibliographic Details
Published in:Journal of fluid mechanics 2015-04, Vol.768, p.549-571
Main Authors: Nair, Aditya G., Taira, Kunihiko
Format: Article
Language:English
Subjects:
Analysis
Biological analysis
Brain
Circuits
Electric power grids
Electrical engineering
Epidemics
Graph representations
Graph theory
Graphical representations
Malformations
Network analysis
Risk groups
Social networks
Social organization
Subgroups
Variables
Vortices
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Summary:We examine discrete vortex dynamics in two-dimensional flow through a network-theoretic approach. The interaction of the vortices is represented with a graph, which allows the use of network-theoretic approaches to identify key vortex-to-vortex interactions. We employ sparsification techniques on these graph representations based on spectral theory to construct sparsified models and evaluate the dynamics of vortices in the sparsified set-up. Identification of vortex structures based on graph sparsification and sparse vortex dynamics is illustrated through an example of point-vortex clusters interacting amongst themselves. We also evaluate the performance of sparsification with increasing number of point vortices. The sparsified-dynamics model developed with spectral graph theory requires a reduced number of vortex-to-vortex interactions but agrees well with the full nonlinear dynamics. Furthermore, the sparsified model derived from the sparse graphs conserves the invariants of discrete vortex dynamics. We highlight the similarities and differences between the present sparsified-dynamics model and reduced-order models.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2015.97