IV Stability of non-straight jets

In section §5, we discussed the possible mechanisms which directly affect the shape of a jet. However, these mechanisms may not last for a long time and may result in instabilities. The most obvious problem would be if the collimation of the jet were no longer achieved efficiently. This occurs when the Mach number of the flow decreases to such an extent that it becomes subsonic. The most natural way of making a supersonic flow to become subsonic is through the creation of a strong discontinuity in the hydrodynamical quantities, that is, through a shock wave.

When a jet bends it is naturally in direct contact with its surroundings and entrainment from the external gas might cause disruption to its structure (Icke, 1991). However, if that problem is bypassed, for example, by an efficient cooling, there remains a high Mach number collimated flow within a curved jet. When a supersonic flow bends, the characteristics emanating from it tend to intersect at a certain point in space (Courant & Friedrichs, 1976; Landau & Lifshitz, 1995). Since the hydrodynamical values of the flow along non-parallel characteristic lines have different constant values, this intersection causes the different values of these quantities to be multivalued. This situation cannot occur in nature and a shock wave is formed to overcome this problem.

The formation of internal shocks inside the jet is potentially extremely dangerous since the flow behind the shock is subsonic and collimation is no longer possible. If the characteristics intersect outside the jet, then a shock wave is not formed and it seems that in this case the jet can survive a bending. However, as will be shown in this chapter, the Mach number decreases in a bend and the rate of change of the Mach angle with respect to the bending angle, defined as the angle the jet makes with its original straight trajectory, increases without bounds as the Mach number tends to unity. This means that there is a stage in which the Mach angle increases faster than the bending angle. This causes the characteristics in the jet to intersect and form a terminal shock. The aim of this chapter is to investigate these physical mechanisms, in particular, to investigate the formation of internal shocks in the structure of a jet.