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Strong observational evidence indicates that all extragalactic jetsassociated with AGNs move at relativistic speed up to 100 pc - 1 kpc scalesfrom the nucleus. At larger distances, reflecting the Fanaroff-Riley radiosource classification, we observe an abrupt deceleration in FR-I jets whilerelativistic motions persist up to Mpc scale in FR-II. Moreover, VLBIobservations of some object like B2 1144+35, Mrk501 and M87 show limbbrightening of the jet radio emission at the parsec scale. This effect isinterpreted kinematically as due to the presence of a deboosted central spineat high Lorentz factor and of a weakly relativistic external layer. In thispaper we investigate whether these effects can be interpreted by a breaking ofthe collimated flow by external medium entrainment favored by shearinstabilities, namely Kelvin-Helmholtz instabilities. We examine in details thephysical conditions under which significant deceleration of a relativistic flowis produced. We investigate the phenomenon by means of high-resolutionthree-dimensional relativistic hydrodynamic simulations using the PLUTO codefor computational astrophysics. We find that the parameter of utmost importancein determining the instability evolution and the entrainment properties is theambient/jet density contrast. We show that lighter jets suffer stronger slowingdown in the external layer than in the central part and conserve a centralspine at high Lorentz factor. Our model is verified by constructing syntheticemission maps from the numerical simulations that compare reasonably well withVLBI observations of the inner part of FR-I sources.

Formation of dynamical structures in relativistic jets: the FRI case