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Polarized vortex reconnection

Published online by Cambridge University Press:  12 July 2021

Jie Yao Open the ORCID record for Jie Yao [Opens in a new window]  and
Fazle Hussain Open the ORCID record for Fazle Hussain [Opens in a new window]
Jie Yao
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX79409, USA
Fazle Hussain*
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX79409, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 922 , 10 September 2021 , A19
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© The Author(s), 2021. Published by Cambridge University Press

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Yao and Hussain supplementary movie 1

Isosurface of vorticity magnitude shaded with contours of axial vorticity for counter-polarized cases at Re=5000.

Download Yao and Hussain supplementary movie 1(Video)
Video 5.3 MB

Yao and Hussain supplementary movie 2

Isosurface of vorticity magnitude shaded with contours of axial vorticity for co-polarized cases at Re=5000.

Download Yao and Hussain supplementary movie 2(Video)
Video 11.3 MB

Yao and Hussain supplementary movie 3

Isosurface of vorticity magnitude shaded with contours of axial vorticity for counter-polarized q=1 cases at Re=9000.

Download Yao and Hussain supplementary movie 3(Video)
Video 2.4 MB

Yao and Hussain supplementary movie 4

Isosurface of vorticity magnitude shaded with contours of axial vorticity for co-polarized q=1 cases at Re=9000.
Download Yao and Hussain supplementary movie 4(Video)
Video 3.4 MB