Viscous and inviscid reconnection of vortex rings on logarithmic lattices

To address the possible occurrence of a finite-time singularity during the oblique reconnection of two vortex rings, (Moffatt and Kimura 2019, J. Fluid Mech., vol. 870, R1) developed a simplified model based on the Biot–Savart law and claimed that the vorticity amplification $\omega _{{max}}/\omega _0$ becomes very large for vortex Reynolds number $Re_{\varGamma } \geqslant 4000$ . However, with direct numerical simulations (DNS), Yao and Hussain (2020 a , J. Fluid Mech. vol. 888 , pp. R2) were able to show that the vorticity amplification is in fact much smaller and increases slowly with $Re_{\varGamma }$ . This suppression of vorticity was linked to two key factors – deformation of the vortex core during approach, and formation of hairpin-like bridge structures. In this work, a recently developed numerical technique called log-lattice (Campolina & Mailybaev, 2021, Nonlinearity , vol. 34, 4684), where interacting Fourier modes are logarithmically sampled, is applied to the same oblique vortex ring interaction problem. It is shown that the log-lattice vortex reconnection displays core compression and formation of bridge structures, similar to the actual reconnection seen with DNS. Furthermore, the sparsity of the Fourier modes allows us to probe very large $Re_{\varGamma } = 10^8$ until which the peak of the maximum norm of vorticity, while increasing with $Re_{\varGamma }$ , remains finite, and a blow-up is observed only for the inviscid case.