  A model is developed describing the approach to a finite-time singularity of
the Navier-Stokes equations for two interacting vortices. The model is derived
from a combination of the Biot-Savart law and an equation describing the
evolution of the vortex core cross-sections. A nonlinear dynamical system is
derived for the minimum separation parameter $s(\tau)$, the curvature
$\kappa(\tau)$, and the radial scale $\delta(\tau)$ of the vortex cross-section
at the points of closest approach, where $\tau$ is dimensionless time. The
scaling properties of this system are investigated.
