Near-singular collapse and local intensification of a ‘‘Lissajous-elliptic’’ vortex ring: Nonmonotonic behavior and zero-approaching local energy densities

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Abstract
This Letter observes collapse and intensification of the two parameter (b,c) ‘‘Lissajous-elliptic’’ vortex ring. Laboratory and direct numerical studies of this ring are proposed to elucidate near-singular and intermittent fluid phenomena at very high Reynolds number. Quantifications of single filament Biot–Savart numerical simulations with various core ‘‘radii’’ show that collapse may be nonmonotonic in time. In the collapsing region, the largest positive strain-rate eigenvalue, α, is off the filament and exhibits self-similar, singular-like behavior. A signature of collapse is found in the local approach to zero of the filament energy density in the collapsing regions.

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