  We study the interplay between the local geometric properties and the
non-blowup of the 3D incompressible Euler equations. We consider the
interaction of two perturbed antiparallel vortex tubes using Kerr's initial
condition \cite{Kerr93}[Phys. Fluids {\bf 5} (1993), 1725]. We use a
pseudo-spectral method with resolution up to $1536\times 1024 \times 3072$ to
resolve the nearly singular behavior of the Euler equations. Our numerical
results demonstrate that the maximum vorticity does not grow faster than double
exponential in time, up to $t=19$, beyond the singularity time $t=18.7$
predicted by Kerr's computations \cite{Kerr93,Kerr04}. The velocity, the
enstrophy and enstrophy production rate remain bounded throughout the
computations. As the flow evolves, the vortex tubes are flattened severely and
turned into thin vortex sheets, which roll up subsequently. The vortex lines
near the region of the maximum vorticity are relatively straight. This local
geometric regularity of vortex lines seems to be responsible for the dynamic
depletion of vortex stretching.
