Energy and enstrophy cascade during reconnection of orthogonally interacting vortex tubes

Viscous reconnection of initially orthogonal vortex tubes with both equal and unequal circulation strengths is investigated through direct numerical simulations. The vortex tubes are initially perturbed into a locally anti-parallel configuration due to mutual induction and then start to reconnect under self-induction. In the equal-strength case, the reconnection dynamics closely resembles that reported by Yao and Hussain [“Polarized vortex reconnection,” J. Fluid Mech. 922, A19 (2021)] for co-polarized anti-parallel vortex tubes (i.e., with opposing axial flows). With increasing vortex Reynolds numbers Re (≡ Γ₀/ν, circulation/viscosity), more fine-scale structures are generated around the bridges and threads, forming a − 7/3 inertial range for the kinetic energy spectrum. In the unequal-strength case, broken symmetry leads to more complex topological evolution, with vortex bursting observed after reconnection. The total helicity decreases rapidly during both reconnection and bursting. In particular, as the circulation disparity increases, the intensity of structures with negative helicity densities becomes more pronounced. The transfer, production, and dissipation of energy and enstrophy are examined via filtering the velocity field in bands of wavenumbers distributed logarithmically in Fourier space. Similar to homogeneous isotropic turbulence, the energy and enstrophy are predominantly transferred from large to small scales, particularly between the adjacent bands. Interestingly, an inverse cascade of energy to large scales is observed during and after equal-strength reconnection, which is due to the accumulation of bridgelets to form large-scale bridges. Moreover, with increasing circulation mismatch, forward energy and enstrophy transfers shift toward lower modes, indicating the breakup of larger structures, which may inform the strategy for accelerating the dissipation of aircraft wake vortices.