Fig. 1a: A 2D axisymmetric simulation of a marginally relativistic flow (v = 0.3c) with Mach number M = 6 and adiabatic index Γ = 5/3. The jet enters from the left and in penetrating a medium in pressure balance with it, but with a density ×10 that of the jet, drives a bow shock ahead of it. Kelvin-Helmholtz instability at the contact surface between the shocked jet and shocked ambient material sends pressure perturbations into the jet, driving unstable modes of oscillation of the jet, which steepen to form a pattern of incident and reflection shocks.

Fig. 1b: A 2D axisymmetric simulation of a relativistic flow (Lorentz factor, γ = 5) with Mach number M = 17 and adiabatic index Γ = 5/3. The situation is similar to that seen in Fig. 1a, but the relativistic flow is far less prone to instability, in part because of its high effective mass.

Fig. 1c: A 2D axisymmetric simulation of a relativistic flow (Lorentz factor, γ = 5) with Mach number M = 4 and adiabatic index Γ = 5/3. The situation is similar to that seen in Fig. 1b, but the hot, shocked ambient medium expands rapidly, to rethermalize its energy at the secondary (backward sloping) shocks behind the jet head. Contrary to expectation, in this low Mach number flow negligible instability is evident; this is because of weak coupling between the available modes of the jet, and the perturbations capable of driving them.

Fig. 2: A sequence of slices showing the evolution of a jet with γ = 5, Mach number M = 8 and adiabatic index Γ = 5/3, with the inflow precessing on a cone of semiangle π/6 rad, with rate 0.2885 rad per light crossing time of the inflow radius. This fully 3D simulation shows that the jet flow is substantially disrupted about half-way to the bow, but that a core of high momentum flux does persist – the jet has not wholly lost its integrity.