  The linear and non-linear stability of sheared, relativistic planar jets is
studied by means of linear stability analysis and numerical hydrodynamical
simulations. Our results extend the previous Kelvin-Hemlholtz stability studies
for relativistic, planar jets in the vortex sheet approximation performed by
Perucho et al. (2004a,b) by including a shear layer between the jet and the
external medium and more general perturbations. The models considered span a
wide range of Lorentz factors ($2.5-20$) and internal energies ($0.08 c^2-60
c^2$) and are classified into three classes according to the main
characteristics of their long-term, non-linear evolution. We observe a clear
separation of these three groups in a relativistic Mach-number Lorentz-factor
plane. Jets with a low Lorentz factor and small relativistic Mach number are
disrupted after saturation. Those with a large Lorentz factor and large
relativistic Mach number are the stablest, due to the appearance of short
wavelength resonant modes which generate local mixing and heating in the shear
layer around a fast, unmixed core, giving a plausible solution for the problem
of the long-term stability of relativistic jets. A third group is present
between them, including jets with intermediate values of Lorentz factor and
relativistic Mach number, which are disrupted by a slow process of mixing
favored by an efficient and continuous conversion of kinetic into internal
energy. In the long term, all the models develop a distinct transversal
structure (shear/transition layers) as a consequence of KH perturbation growth,
depending on the class they belong to. The properties of these shear layers are
analyzed in connection with the parameters of the original jet models.
