Emergence of coherent patterns of vortex stretching during reconnection: A scattering paradigm

Abstract

We have observed coherent patterns of the magnitude of the normalized vortex stretching vector \<o-Vu|/|fi>| during the "bursting" reconnection phase of the evolution of identical initially orthogonally offset vortex tubes. We propose that the intensification and reconnection of initially tubelike vortex regions be viewed as a scattering process and that the topology of vortex lines during this phase of the process contributes to limiting vortex stretching (intensification). Furthermore, we advocate the use of these patterns (some rendered in color) as signatures of turbulent intermittency in exploring massive data sets. 47.15.Ki Interacting tubelike vortex regions are an ever-present fluid-dynamical phenomenon. They are observed in the vapor-dyed wing-tip vortices of steady [1] and maneuvering [2] aircraft, in the wing-tip vortices of pitching and plunging airfoils [3], in boundary layers as "hairpin" and "ringlike" vortex structures [4], and in simulations of liquid-helium turbulence with local induction vortex filament models ).If two tubelike vortex regions are sufficiently close together or are convected towards each other, they form a "scattering" reconnection configuration. That is, we consider the ingoing state of the scattering process to originate from two straight, well-separated, nonintersecting vortex tubes of compact support with relative angle 0/, O°<0/< 180°.Many studies of vortex reconnection have been initialized with the perturbed antiparallel configuration (0/ = 180°), since they were motivated by the contrail problem and the intermediate time evolution of the Crow instability [8]. We prefer the orthogonally offset (0/ =90°) configuration, which yields a high effective resolution within a given domain. Our selection is motivated by the works of Melander and Zabusky [9,10], who observed intensification and reconnection with this configuration but did not explore the essential dynamics.In both perturbed antiparallel and orthogonally offset initial conditions, initially compact tubes of equal or nearly equal circulation evolve into an ingoing state where a highly intensified dipolar vortex "pancake" forms in a small domain (Pumir and Siggia [11], and Boratav, Pelz, and Zabusky [12,13]). For 0, =90°, there is also a well-defined outgoing state. Thus, we advocate a scattering paradigm to focus attention on the physical processes which occur in the "complex" core state. Within this temporal interval, coherent spatial patterns form which provide alternate signatures for reconnection and turbulent intermittency.A Biot-Savart model with a cutoff was used by Dhanak and de Bernadinis [14] to study the close approach of tubes during the evolution of a high-aspect-ratio elliptical ring. Siggia [15] also used the Biot-Savart model and referred to the ingoing phase as one of "collapse and amplification" but did not employ topological reconnection of filaments nor emphasize the scattering process. Such models fail when the cores overlap with each other as occurs just prior to the reconnection phase.We de...

Flow structures in cerebral aneurysms

“…Other measures of describing the flow field are varied, including vorticity stretching [49] or lumped vorticity rings [43]. Since the circulation is constant for a closed curve group of fluid elements in the absence of rotational external forces, from Kelvin's law, a corollary from Helmholtz second law, and also from Helmholtz first law stating that the strength of a vortex filament is constant along its length then, tracking the lumped vorticity ring over limited distances (before large distortions occur) will allow for a qualitative representation of the flow dynamics with respect to the vortex structure.…”

Vortex tube reconnection at Re = 104

“…A number of simulations, predominantly based on spectral methods, have described the different phases of the reconnection process for Re in the range 1000-3500. These studies include reconnections of vortex rings, [13][14][15][16] anti-parallel tubes, [17][18][19][20] anti-parallel tubes with an orthogonal offset [21][22][23][24] as well as other configurations leading to interesting topological dynamics. 15,25,26 The head-on collision of two vortex rings has been studied experimentally and numerically.…”

Scattering of Superfluid Vortex Rings

“…Finally, many of the vortex scattering results here resemble the NS results-the shape evolution in annihilation and the initial stages of oblique collision are the same, although the latter calculations have not reached the stage of isolated final rings. Note that while the previously established reconnection mechanism [5,19] makes the existence of multiring final states plausible, their detailed evolution requires multiple reconnections, some on length scales comparable to the core size, and the numerical calculations presented here are needed to determine which final states actually occur. The role of quantum mechanics in such processes is to limit possible core sizes and values of circulation to specific values, and in general to smooth the reconnection process (compare [5] to the NS analog in [19]).…”

“…Note that this is a scattering process in the standard quantum mechanical sense: initially there is a "free particle" state containing two separated circular rings moving essentially independently of each other, which upon close approach form a new and nontrivial "interacting" quantum state, which in turn decays to a different free particle state containing two new rings. The analogy to scattering was first made for vortex filament interactions in cosmological string models in 2D [18], and then for NS filaments in 3D [19], but only in the ring cases do the initial and final states correspond to localized particles.…”