  We study the diffusive motion of low-energy normal quasiparticles along the
core of a single vortex in a dirty, type-II, s-wave superconductor. The physics
of this system is argued to be described by a one-dimensional supersymmetric
nonlinear sigma model, which differs from the sigma models known for disordered
metallic wires. For an isolated vortex and quasiparticle energies less than the
Thouless energy, we recover the spectral correlations that are predicted by
random matrix theory for the universality class C. We then consider the
transport problem of transmission of quasiparticles through a vortex connected
to particle reservoirs at both ends. The transmittance at zero energy exhibits
a weak localization correction reminiscent of quasi-one-dimensional metallic
systems with symmetry index beta = 1. Weak localization disappears with
increasing energy over a scale set by the Thouless energy. This crossover
should be observable in measurements of the longitudinal heat conductivity of
an ensemble of vortices under mesoscopic conditions. In the regime of strong
localization, the localization length is shown to decrease by a factor of 8 as
the quasiparticle energy goes to zero.
