Numerical study of the diffusion-like decay of vortex tangles without mutual friction

The diffusion-like decay of vortex tangles without mutual friction is simulated numerically using the localized induction approximation. This algorithm, previously developed by the authors, is based on an examination of crossing lines, and has been used to study vortex reconnection processes. We have examined the effect of various factors on the decay of inhomogeneous vortex tangles: diffusion (large vortex loops break up into smaller ones which move away from an initial volume), changes in length owing to reconnection processes, the elimination of small vortices below the spatial resolution, and the insertion and removal of points to ensure stability of the numerical algorithm. The simulations show that a vortex tangle initially localized in a small region will spread into the surrounding space. The time evolution of the vortex line density inside the initial region agrees satisfactorily with that obtained by solving a diffusion equation. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3604559]