What can two vortex tubes tell us about the turbulent cascade?

We numerically explore the violent interaction of two parallel, counter-rotating vortex tubes which causes the transfer of energy from the initial large, smooth tubes to the late-stage small ``worm''-like structures similar to those in Homogeneous Isotropic Turbulence simulations. Reynolds numbers of up to Re=Γ/ν=6000 are reached, where Γ is the is the vortex ring circulation, and ν the kinematic viscosity of the fluid. When the tubes are initially very close, their deformation is due to the elliptical instability. The tubes generate perpendicular filaments which undergo transformations of filaments into sheets into filaments, according to an iterative cascade of the type suggested by Brenner et al. (Phys. Rev. Flu., 1, 084503 (2016)). By numerically introducing different perturbations, we compare the dynamics resulting from the elliptical instability, to that induced by the Crow-like instabilities, which lead to reconnection. We show that the iterative mechanisms, triggered by the elliptical instability, transfers energy across scales much more efficiently as a whole than reconnection. We propose that this iterative mechanism is crucial for understanding the turbulent cascade.