Spatial stability of relativistic jets - Application to 3C 345

The relativistic dispersion relation describing the growth and propagation of the harmonic components of a perturbation to the surface of a cylindrical relativistic jet are analyzed numerically for relativistic flows. The results are used to extend previous expressions for resonant frequencies, wavelengths, and the maximum growth rate at resonance valid for nonrelativistic flows to relativistic flows. The results are used to develop a model for the helical twisting of a light relativistic jet expanding in response to an external pressure gradient. The model equations are applied to observed motions of the components in the jet in 3C 345 to show how a light, helically twisted jet produced by the Kelvin-Helmholtz instability can explain the apparent motions and accelerations of components along the jet in 3C 345.