  Strong observational evidence indicates that all extragalactic jets
associated with AGNs move at relativistic speed up to 100 pc - 1 kpc scales
from the nucleus. At larger distances, reflecting the Fanaroff-Riley radio
source classification, we observe an abrupt deceleration in FR-I jets while
relativistic motions persist up to Mpc scale in FR-II. Moreover, VLBI
observations of some object like B2 1144+35, Mrk501 and M87 show limb
brightening of the jet radio emission at the parsec scale. This effect is
interpreted kinematically as due to the presence of a deboosted central spine
at high Lorentz factor and of a weakly relativistic external layer. In this
paper we investigate whether these effects can be interpreted by a breaking of
the collimated flow by external medium entrainment favored by shear
instabilities, namely Kelvin-Helmholtz instabilities. We examine in details the
physical conditions under which significant deceleration of a relativistic flow
is produced. We investigate the phenomenon by means of high-resolution
three-dimensional relativistic hydrodynamic simulations using the PLUTO code
for computational astrophysics. We find that the parameter of utmost importance
in determining the instability evolution and the entrainment properties is the
ambient/jet density contrast. We show that lighter jets suffer stronger slowing
down in the external layer than in the central part and conserve a central
spine at high Lorentz factor. Our model is verified by constructing synthetic
emission maps from the numerical simulations that compare reasonably well with
VLBI observations of the inner part of FR-I sources.
