Fluid flow and particle dispersion were investigated numerically in the wavy vortex regime of Taylor-Couette flow. The flow field for wavy vortex flow is stationary when viewed in a frame rotating with the azimuthal wave velocity These steady flow fields are used to track fluid particles and to estimate the effective axial diffusion resulting from chaotic fluid advection. The effective diffusion coefficient for a fixed wave state is a function of the Reynolds number. Particle dispersion is a strong function of wave state, showing that a universal relationship between dispersion and Reynolds number cannot be found in this regime of cylindrical Taylor-Couette flow. The effective Schmidt number of chaotic advection is less than unity for all wavy vortex flows examined, indicating that chaotic advection plays an important role in fluid mixing in these flow regimes. Fluid particle retention in the cores of the wavy vortices is also predicted for some parameter regimes, although not all. Particles trapped in vortex cores are only poorly mixed within the core and play no role in global mixing. A preliminary examination of inertial particle settling suggests that the fluid flow does not prevent settling in the mean, although the magnitude of the settling velocity significantly affects the dispersion of inertial particles.