Study of the Three Dimensional Eular Equations

Investigating the behavior of antiparallel vortex tubes using numerical simulations

Abstract

Three-dimensional, incompressible Eulercalculations of the interaction of perturbed antiparallel vortex tubes usingsmooth initial profiles in a bounded domain with bounded initial vorticity arediscussed. A numerical method that uses symmetries and additional resolution inthe direction and location of maximum compression is used to simulate periodicboundary conditions in all directions. For an initial condition that yieldssingular behavior, the growth of the peak vorticity, the peak axial strain, andthe enstrophy production obey  (tc-t)-land the enstrophy grows logarithmically. The enstrophy growth is associatedwith the energy spectrum approaching k-3.Self-similar development and equal rates of collapse in all three directionsare shown.