Polarized vortex reconnection. (10th September 2021)

• Record Type: Journal Article
• Authors: Yao, Jie; Hussain, Fazle
• Is Part Of: Journal of fluid mechanics. Volume 922(2021)
• Publication Date: 2021-09-10
• Subjects: vortex dynamics -- vortex interactions; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2021.517
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : 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 $Re$ ( $\equiv \varGamma /\nu$ ) 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. $\pm h$ ) 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.