All Tables

Table 1: Equilibrium parameters of different simulated jet models. The meaning of the symbols is as follows. $\gamma$ : jet flow Lorentz factor; $\varepsilon$ : specific internal energy; $c_{\rm s}$ : sound speed; p: pressure; $\nu$ : jet-to-ambient relativistic rest mass density contrast; $\eta$ : jet-to-ambient enthalpy contrast; M_j: jet relativistic Mach number; k_0,1,2,3: excited longitudinal wavenumbers. Labels a and j refer to ambient medium and jet, respectively. All the quantities in the table are expressed in units of the ambient density $\rho _{0a}$ , the speed of light c, and the jet radius R_j.
Table 2: Dominant modes in the linear phase of the numerical simulations. w_{i,k_j}: maximum growth rate for the jth overtone wavenumber excited in the simulation (see Table 1) derived from linear stability analysis. Left columns: symmetric mode; right columns: antisymmetric one. The dominant mode refers to the mode with the largest amplitude in rest mass density perturbation as derived from Fourier analysis of the box, written from larger to smaller amplitude when more than one is present. w_i: fitted pressure perturbation growth rate for the linear regime in the simulation. Growth rate values are in c/R_j units. *: models where irregular growth affects the evolution (see text).
Table 3: Growth of resonant modes. Models which present a global maximum growth rate (according to the linear analysis) for all resonant modes (i.e., at any wavelength) above the growth rates of the perturbed modes are listed. $w_{i,\rm max}$ : maximum growth rate for all resonant modes from linear analysis; $w_{i,p,v_{\perp}}\!$ : fitted growth rates of pressure and perpendicular velocity perturbations for the fast growth linear regime in the simulation, only for those simulations where it occurs; $w_{i,\parallel }$ : same as $w_{i,p,v_{\perp }}$ for axial velocity. All values are in c/R_j units.
Table 4: Times for the different phases in the evolution of the perturbed jet models. $t_{\rm lin}$ : end of linear phase (the amplitudes of the different quantities are not constant any longer). $t_{\rm sat}$ : end of saturation phase (the amplitude of the transverse speed perturbation reaches its maximum). $t_{\rm mix}$ : the tracer starts to spread. $t_{\rm peak}$ : the peak in the amplitude of the pressure perturbation is reached. $t_{\rm mex}$ : the jet has transferred to the ambient 1% of its initial momentum. $\Delta _{\rm peak}$ : relative value of pressure oscillation amplitude at the peak of pressure perturbation (see Fig. 3).