Enstrophy growth during asymmetrical reconnection of vortex tubes with logarithmic lattices

Logarithmic lattices (or log-lattice in short) is a spectral numerical technique developed by Campolina and Mailybaev [2021, Fluid dynamics on logarithmic lattices, Nonlinearity] where the discrete Fourier modes are spaced out logarithmically. The Navier-Stokes or Euler equations in their exact original form are projected on this sparse Fourier lattice, allowing one to preserve the main symmetries and conservation laws of the equations without the need for adjustable parameters. The logarithmic spacing also allows one to reach very large Reynolds numbers with few modes, thereby reducing the computational cost. In recent work, Harikrishnan et al., [2025, Viscous and Inviscid Reconnection of Vortex Rings on Logarithmic Lattices, arXiv:2502.19005] have shown that it can be used as a toy model for vortex reconnection studies as it appears to retain many qualitative and quantitative attributes seen with direct numerical simulations (DNS). The maximum growth of enstrophy is studied for increasingly asymmetrical reconnection of vortex tubes (by introducing axial flow in the cores, changing the amplitude of the perturbation etc.) at very large Reynolds numbers. Results from this toy model could have direct implications on the bounds of enstrophy growth for the full Navier-Stokes problem.