Significant insight into the physics of extragalactic radio sources has come through numerical simulations. Reviews of such results can be found in Norman (1989), Williams (1991), and Clarke (1990, 1992). We briefly consider some of the more important results as they apply to sources such as Cygnus A.
The basic structure of supersonic jets, hotspots, and radio lobes were delineated in the early work of Norman et al. (1982). These two-dimensional, axisymmetric hydrodynamic simulations showed the development of the double shock structure at the jet terminus (Mach disk and bow shock), and the evolution of the radio lobe, or `cocoon' of shocked jet material enveloping the jet. A fundamental conclusion from these simulations was that well developed radio lobes, with widths much larger than the jet width, only result from very under-dense jets ( = jet density/external density < 0.1), with high internal Mach numbers (M > 6). In this case the advance speed of the terminal Mach disk is much less than the jet speed thereby requiring a `waste-bin' for the shocked jet material, i.e. the radio lobe. The beam stability is greatly enhanced by the development of this low-density cocoon within which the jet is over-dense, and hence essentially ballistic (Icke 1991). The pressure gradient between the hotspot and lobe may drive a `back-flow' of waste jet material towards the nucleus.
Non-axisymmetric `slab', or full three-dimensional (3D), simulations have answered the interesting issue of multiple hotspots in powerful radio galaxies by allowing for jets which alter direction on time-scales shorter than the radio source lifetime (Williams and Gull 1985, Hardee and Norman 1990, Cox et al. 1991), lending credence to the simple `dentist drill' idea of Scheuer (1982). Such models also result in larger lobe-to-jet width ratios than in axisymmetric models, since the working surface of the jet acts over a much larger area at the head of the lobe as a function of time.
Simulations including dynamically passive magnetic fields result in total and polarized intensity distributions which match the observations reasonably well (Clarke 1992, Mathews and Scheuer 1991), including `hamburger hotspots' at the terminal Mach disks, high fractional polarizations along source edges, and filamentary structures in radio lobes. Simulations involving dynamically important fields result in a prominent `nose-cone' of emission beyond the terminal Mach disk, and no development of a radio cocoon (Clarke 1992; Clarke et al. 1989, Lind et al. 1989). Neither of these features is consistent with the observed structures in sources such as Cygnus A. Overall, Clarke (1992) concludes that most of the structures of FRII radio galaxies can be explained reasonably within the context of 3D simulations of light, fast jets which alter direction by small angles on fairly short time-scales, and within which the magnetic fields are not dynamically dominant.