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Polarized vortex reconnection
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DOI：10.1017/jfm.2021.517.png)
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Abstract
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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 Re (equivalent to Gamma/.) up to 9000 and initial polarization strength q (ratio of peak axial to azimuthal velocities) between 0 and 4/3. For both counter- and co-polarized cases, although the reconnection is delayed as q increases - mainly due to weakened self-induction - it is more rapid and more complete for small q. Enstrophy growth and energy cascade are suppressed for weak polarization (q < 1/2) due to depleted nonlinearity, but are enhanced for strong polarization (q > 1/2) due to instability and/or transient growth. When counter-polarized, numerous structures with both positive and negative helicity densities (i.e.+/- h) are generated. For large q, strong axial flows opposite to the initial flows occur - causing polarization reversals. For the co-polarized cases, although +h predominates, -h structures also form and interact with positive ones - leading to helicity cascade to small scales. As Re 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 q alters the energy spectrum in the inertial range with a scaling varying from k(-5/)3 for the unpolarized case to k(-7/3) for the strongly polarized case, which seems to be associated with the enhanced vortex spiralling. In addition, for the strongly co-polarized cases, a k(-4/3) helicity spectrum develops. Furthermore, most of the energy and helicity in the inertial range with scale L transfer to scales between 0.3L and 0.4L. Therefore, polarization can significantly alter the dynamics of vortex reconnection as well as turbulence cascade.
Keywords:
vortex dynamics
vortex interactions
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