Since the pioneering work by Norman et al. (1982), many numerical studies have been devoted to the analysis of the propagation of a supersonic jet shot into an ambient medium (see Massaglia, Bodo & Ferrari 1995, hereinafter Paper I, and references therein). In spite of these strong efforts many aspects of this problem are still not well understood. This is due to the complexity of the jet-cocoon structure: in fact, the cocoon excites perturbations to the jet flow, which in turn can be amplified by the Kelvin–Helmholtz mechanism and induce a strong activity of the jet's head that affects the cocoon structure. Thus a complex feedback loop mechanism establishes between jet and cocoon which make the dynamics of the interaction very complex.