Polarized vortical structures (i.e. with axial flow, thus coiled vortex lines) are generic to turbulent flows - hence the importance of their dynamics, interactions and cascade. Direct numerical simulations of two anti-parallel polarized vortex tubes are performed for vortex Reynolds numbers up to and initial polarization strength (ratio of peak axial to azimuthal velocities) between and. For both counter- and co-polarized cases, although the reconnection is delayed as increases - mainly due to weakened self-induction - it is more rapid and more complete for small. Enstrophy growth and energy cascade are suppressed for weak polarization due to instability and/or transient growth. When counter-polarized, numerous structures with both positive and negative helicity densities (i.e.) due to depleted nonlinearity, but are enhanced for strong polarization (1/2) are generated. For large, strong axial flows opposite to the initial flows occur - causing polarization reversals. For the co-polarized cases, although predominates, structures also form and interact with positive ones - leading to helicity cascade to small scales. As increases, small scales are more numerous: for counter-polarized cases, the threads undergo successive reconnections in a cascade - akin to the unpolarized case; for co-polarized cases, the newly formed vortex ring breaks up with numerous hairpin vortices wrapping around it. Increasing alters the energy spectrum in the inertial range with a scaling varying from for the unpolarized case to for the strongly polarized case, which seems to be associated with the enhanced vortex spiralling. In addition, for the strongly co-polarized cases, a helicity spectrum develops. Furthermore, most of the energy and helicity in the inertial range with scale transfer to scales between and. Therefore, polarization can significantly alter the dynamics of vortex reconnection as well as turbulence cascade.
- vortex dynamics
- vortex interactions