General relativistic hydrodynamics with special relativistic Riemann solvers

In this paper we continue investigations of the Kelvin-Helmholtz instability of stratified jets. We first general- ize our previous analytical results by taking into consideration relativistic motion and relativistic equation of states for the three components namely the inner beam, the sheet or envelope and the ambient medium, and derive the dispersion relation for the Kelvin-Helmholtz instability. The ultrarelativistic limit of pa- per I as well as the nonrelativistic limit for both the equations of state and the jet bulk speed can be deduced. Exploring a wider range of parameters, we find evidence for two main types of instability modes, with mode crossing and interaction between modes. These two modes correspond to the excitation of sound waves in the beam and in the envelope which can both act as a resonant wave guide. As a result, the addition of an inner beam inside a jet can strongly enhance the linear growth of its Kelvin- Helmholtz instability. The stratified jet scenario appears quite relevant to give account for the complex morphology and ve- locity fields now observed in a few jets such as in M87, where various layers with respect to the jet axis are clearly visible.