Helicity dynamics in viscous vortex links

• DOI: 10.1017/jfm.2022.532
• Publication Date: 2022-07-05T13:43:57Z
• Authors: Jie Yao; Weiyu Shen; Yue Yang; Fazle Hussain
• Keywords: Helicity; Vortex Tube

The dynamics of two slender Hopf-linked vortex rings at Reynolds numbers ( $Re \equiv \varGamma /\nu, \mathrm {circulation/viscosity}$ ) $2000$ , $3000$ and $4000$ is studied using direct numerical simulations the incompressible Navier–Stokes equations. Under self-induction, initially perpendicularly placed approach each other reconnect to form separate rings. leading ring closely cuddled further undergoes secondary reconnection even smaller At high $Re$ subsequent are unstable break up into turbulent clouds consisting numerous smaller-scale structures. Although global helicity $H$ remains constant before reconnection, it increases then rapidly decays during – both growth decay rates increase with . In higher (i.e. 3000 4000) cases, rises after first reaches a quasi-plateau asymptotic value continuously increasing suggesting that for viscous flows not conserved very Further flow analysis demonstrates significant positive negative helical structures simultaneously generated their different main reason complex evolution By examining topological aspects dynamics, we find that, from sum link writhe $L_k+W_r$ drop reconnection. Our results also clearly demonstrate twist, which plays role in particularly