Coherent laminar and turbulent motion of toroidal vortex bundles

Abstract

Motivated by experiments performed in superfluid helium, we study numerically the motion of toroidal bundles of vortex filaments in an inviscid fluid. We find that the evolution of these large-scale vortex structures involves the generalised leapfrogging of the constituent vortex rings. Despite three dimensional perturbations in the form of Kelvin waves and vortex reconnections, toroidal vortex bundles retain their coherence over a relatively large distance (compared to their size), in agreement with experimental observations.Comment: 22 pages, 12 figure

Single and multiple vortex rings in three-dimensional Bose-Einstein condensates: Existence, stability, and dynamics

“…A perhaps more straightforward, although computationally demanding possibility, would be to explore the dynamics of VRs in a way similar to that of Ref. [53]. In this work, the authors use the full BiotSavart law in order to explore the interactions between numerous initially co-axial vortex rings in a uniform medium with the aim of studying their leapfrogging behavior.…”

Three-dimensional stability of leapfrogging quantum vortex rings

“…In this context, a particularly interesting dynamical regime is the so called leapfrogging motion of two or more coaxial vortex rings when they periodically pass through one another infinitely many times, as exemplified in Fig.1 (for a review, see [3,4]). While investigated in detail for idealized axially symmetric configurations, interacting quantum vortex rings with distortions in three dimensions were theoretically considered just in a few recent works [14][15][16][17][18]. In particular, perturbations of vortex ring pairs were studied analytically in [17,18], but with parameters corresponding to short-scale instabilities.…”

“…Numerical simulations of macroscopic-size toroidal vortex bundles in Ref. [15] demonstrated development of three-dimensional (3D) instabilities. In the last case the ratio of central torus radius R 0 to a vortex core width ξ was of order R 0 /ξ ∼ 10 8 , thus corresponding to value of the local induction parameter Λ = ln(R 0 /ξ) ≈ 18.…”

Interactions between normal-fluid and superfluid vortex rings in helium-4

“…This process is not accompanied by the locking of vorticities in the two fluids. This implies that the coherent superfluid vortex bundles studied in [18] must be put in the system "by experimental design", and are not emergent structures of superfluid turbulence. For the case of fully developed turbulence at finite temperature superfluid helium-4, the implication is that, at steady state, homogeneous, isotropic turbulence, the energies in the two fluids are expected to reach an equilibrium with similar but not necessarily equal levels.…”