Oblique collision and reconnection of a vortex ring with a vortex tube

Abstract

The oblique collision and reconnection of a vortex ring and a vortex tube are numerically investigated using a sixth-order accurate vortex-in-cell method. At the oblique collision angle (α) of 0°, the reconnection occurs, in which half of the ring joins with a part of the tube to create a reconnected ring, and another half of the ring links to the rest of the tube to establish a new reconnected tube. At α = 15°, 30°, and 45°, two reconnections take place, where the first one generates a distorted reconnected tube, and then this tube reconnects itself to construct a new ring and a tube. The secondary vortex structures only appear surrounding the reconnected ring at α = 0°, while they are around both the reconnected ring and tube at α = 30° and 45°. As α increases, the time interval τ between two reconnections rises, and it is determined by a quadratic function as τ(α)=0.0037α2+0.0853α+0.975. The energy spectrum of the flow at the wavenumber (k) from 3 to 10 obeys the k−5/3 slope of a fully turbulent flow, and it is independent of α. However, the energy spectrum at the high wavenumber from 10 to 60 depends on α. This energy spectrum approaches the k−5/3 slope after the second reconnection for whole investigated cases.