Dynamics of Quantized Vortices Before Reconnection

Abstract

The main goal of this paper is to investigate numerically the dynamics of quantized vortex loops, just before the reconnection at finite temperature, when mutual friction essentially changes the evolution of lines. Modeling is performed on the base of vortex filament method using the full Biot–Savart equation. It was discovered that the initial position of vortices and the temperature strongly affect the dependence on time of the minimum distance $\delta (t)$ between tips of two vortex loops. In particular, in some cases, the shrinking and collapse of vortex loops due to mutual friction occur earlier than the reconnection, thereby canceling the latter. However, this relationship takes a universal square-root form $\delta \left( t\right) =\sqrt{\left( \kappa /2\pi \right) \left( t_{*}-t\right) }$ at distances smaller than the distances, satisfying the Schwarz reconnection criterion, when the nonlocal contribution to the Biot–Savart equation becomes about equal to the local contribution. In the “universal” stage, the nearest parts of vortices form a pyramid-like structure with angles which neither depend on the initial configuration nor on temperature.