Quantum reconnection of an inclined vortex ring with a straight vortex line: Energy distribution and geometric...

We investigate the reconnection process involving a quantum vortex ring colliding at different angles with a quantum straight vortex line. The dynamics of this phenomenon is well described by the Gross-Pitaevskii equation. Two families of initial configurations are explored, one by varying the angle α between the vortex ring and the horizontal plane, the other by changing the angle σ between the vortex ring and the vertical plane through the straight vortex and the ring center. Results show that sound generation is maximal when the ring is initially parallel to the straight vortex, whereas the kinetic energy is predominantly composed of the incompressible contribution when the angle α is increased. We provide evidence for the existence of a critical angle α[over ¯] above which a gradual decrease in kinetic energy accompanied by an increase in the curvature of the ring after the second reconnection appears. Since curvature is associated with the velocity of the nodal lines, we conclude that the loss of the fluid's incompressible kinetic energy is compensated by the increase in the kinetic energy of the nodal lines. We also observe that for angles greater than α[over ¯], the kinetic and internal energy components exchange their rate, while the quantum energy increases at a constant rate regardless of the angle. Changing the angle σ may result in both reconnection and absorption of the vortex ring, the latter occurring only for a restricted range of negative angles σ. A critical negative value σ[over ¯] is found beyond which the growth rate of the kinetic and internal energy changes sign. This occurs precisely when reconnection is replaced by absorption. We also observe that while changing the sign of α ensures symmetric behavior, changing the sign of σ instead leads to an asymmetry due to the effect of the straight vortex on the ring motion. In particular, for negative values of σ, the fluid kinetic energy decreases because the straight vortex opposes the ring, with a stronger and more evident effect as σ moves to less negative values.