Reconnection of skewed vortices

Abstract

Based on experimental evidence that vortex reconnection commences with the approach of nearly antiparallel segments of vorticity, a linearised model is developed in which two Burgers-type vortices are driven together and stretched by an ambient irrotational strain field induced by more remote vorticity. When these Burgers vortices are exactly antiparallel, they are annihilated on the strain time-scale, independent of kinematic viscosity ν in the limit ν → 0. When the vortices are skew to each other, they are annihilated under this action over a local extent that increases exponentially in the stretching direction, with clear evidence of reconnection on the same strain time-scale. The initial helicity associated with the skewed geometry is eliminated during the process of reconnection. The model applies equally to the reconnection of weak magnetic flux tubes under the action of a strain field, when Lorentz forces are negligible.

Potential singularity mechanism for the Euler equations

“…At low Reynolds numbers, reconnection occurs in a seemingly simple (laminar) way [35][36][37][38][39]. The process can be described by an elegant model [40], which very successfully reproduces the main features observed in low-resolution numerical studies [41].…”

Helicity conservation under quantum reconnection of vortex rings

“…This result is mirrored by the mathematical analysis of conservation of writhe and total torsion (for definitions, see Sec.III here below) under the assumption of antiparallel reconnection of the interacting strands [13]. On the other hand recent numerical results [14], based on a linearized model of interacting Burgers-type vortices brought together by an ambient irrotational strain field, show that the initial helicity associated with the skewed geometry is eliminated during the process. This apparent contradiction motivates further the present study.…”

“…Initial conditions.-A pair of vortex rings is set at the center of the numerical box. While this particular setting provides a good comparative test for the physics of vortex reconnection [22], it helps to avoid difficulties associated with the numerical implementation of boundary conditions and the topological complexity implied by periodic conditions, while offering a realistic match to simulate the event studied in [14]. At each point Q on the vortex ring we place a Frenet triad {t,n,b} given by the local unit tangent, normal and binormal to the vortex centerline (no inflexion points emerge during the simulation).…”

“…In recent months a number of remarkable results based on experimental observations [12], mathematical analysis [13] and theoretical and numerical work [14] have provided contradictory information as regards helicity transfer through reconnection. On one hand laboratory experiments on the production and evolution of vortex knots in water show [12] that the centerline helicity of a vortex filament remains essentially conserved throughout the spontaneous reconnection of the interacting vortices.…”

Helicity, topology, and Kelvin waves in reconnecting quantum knots

“…As a few examples, experiments of vortex knots in water have shown that center line helicity remains constant throughout reconnection events [17], while theoretical arguments indicate that writhe (one component of the helicity) should be conserved in anti-parallel reconnection events [18], a fact later confirmed in numerical simulations of a few specific quantum vortex knots [19]. However, numerical studies of Burgers-type vortices indicate that helicity is not conserved [20]. While experiments studying helicity in quantum flows have not been done yet, the recent experimental creation of quantum knots in a Bose-Einstein condensate in the laboratory [21] is a significant step in that direction.…”