  The stable propagation of jets in FRII sources is remarkable if one takes
into account that large-scale jets are subjected to potentially highly
disruptive three-dimensional (3D) Kelvin-Helmholtz instabilities. Numerical
simulations can address this problem and help clarify the causes of this
remarkable stability. Following previous studies of the stability of
relativistic flows in two dimensions (2D), it is our aim to test and extend the
conclusions of such works to three dimensions. We present numerical simulations
for the study of the stability properties of 3D, sheared, relativistic flows.
This work uses a fully parallelized code Ratpenat that solves equations of
relativistic hydrodynamics in 3D. The results of the present simulations
confirm those in 2D. We conclude that the growth of resonant modes in sheared
relativistic flows could be important in explaining the long-term collimation
of extragalactic jets.
