Title: Network-theoretic approach to sparsified discrete vortex dynamics,
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 for constructing sparsified
models and evaluating the dynamics of vortices in the sparsified setup.
Identification of vortex structures based on graph sparsification and sparse
vortex dynamics are 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 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
the reduced-order models.