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Polarized vortex reconnection
Published online by Cambridge University Press: 12 July 2021
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.
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- © The Author(s), 2021. Published by Cambridge University Press
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![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210709180639157-0712:S0022112021005176:S0022112021005176_inline550.png?pub-status=live)
Yao and Hussain supplementary movie 1
Isosurface of vorticity magnitude shaded with contours of axial vorticity for counter-polarized cases at Re=5000.
Yao and Hussain supplementary movie 2
Isosurface of vorticity magnitude shaded with contours of axial vorticity for co-polarized cases at Re=5000.
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