  We present a formal, approximate model for singularity formation in classical
fluid dynamics in three dimensions. The construction utilizes an approximation
of local two-dimensionality to study an anti-parallel hairpin vortex structure
with a cross-section equivalent to the 2D Chaplygin-Lamb dipole vortex. The
model exhibits a finite time Euler singularity at an isolated point, with only
finite local stretching of vortex lines. The model also suggests an associated
Navier-Stokes problem, which exhibits a finite-time point singularity, provided
that a Reynolds number is sufficiently large. The singularities are compatible
with both the BKM [1] and CF[2] conditions. The vorticity support is infinite
in volume but the singularity forms as a result of local processes requiring
only finite energy input.
