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Network-theoretic approach to sparsified discrete vortex dynamics

Published online by Cambridge University Press:  10 March 2015

Aditya G. Nair  and
Kunihiko Taira
Aditya G. Nair
Affiliation:
Department of Mechanical Engineering and Florida Center for Advanced Aero-Propulsion, Florida State University, Tallahassee, FL 32310, USA
Kunihiko Taira*
Affiliation:
Department of Mechanical Engineering and Florida Center for Advanced Aero-Propulsion, Florida State University, Tallahassee, FL 32310, USA
*
†Email address for correspondence: ktaira@fsu.edu
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Abstract

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.

JFM classification

Mathematical Foundations: Mathematical Foundations Vortex Flows: Vortex dynamics Vortex Flows: Vortex interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 768 , 10 April 2015 , pp. 549 - 571
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Copyright
© 2015 Cambridge University Press 

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