As a fundamental topology-transforming event, reconnection plays a significant role in the
dynamics of plasmas, polymers, DNA, and fluids—both (classical) viscous and quantum …

Helicity, an invariant under ideal-fluid (Euler) evolution, has a topological interpretation in
terms of writhe and twist for a closed vortex tube, but accurately quantifying twist is …

We derive the spin Euler equation for ideal flows by applying the spherical Clebsch
mapping. This equation is based on the spin vector, a unit vector field encoding vortex lines …

Topological transition and helicity conversion of vortex torus knots and links are studied
using direct numerical simulations of the incompressible Navier–Stokes equations. We find …

The dynamics of two slender Hopf-linked vortex rings at vortex Reynolds numbers ($
Re\equiv\varGamma/\nu,\mathrm {circulation/viscosity} $) $2000 $, $3000 $ and $4000 $ is …

We propose the helicity-conserved Navier–Stokes (HCNS) equation by modifying the non-
ideal force term in the Navier–Stokes (NS) equation. The corresponding HCNS flow has …

Using an improved numerical code we investigate the creation and evolution of quantum
knots and links as defects of the Gross–Pitaevskii equation. The particular constraints put on …

We simulate the head-on collision between vortex rings with circulation Reynolds numbers
of 4000 using an adaptive, multiresolution solver based on the lattice Green's function. The …

Particle-grid dual discretization methods employ one group of Lagrangian particles and one
set of background grid, which demonstrate attractive properties because they inherit both the …

Polarized vortical structures (ie with axial flow, thus coiled vortex lines) are generic to
turbulent flows–hence the importance of their dynamics, interactions and cascade. Direct …